Angle problems reward recognizing the right relationship fast. This lesson test gives you 20 original ASVAB-style questions from the Angles and Lines lesson to practice exactly that: intersecting lines, complementary and supplementary expressions, corresponding and same-side interior angles, bisectors, angles on a line and rotations around a point.
Correct answer: Obtuse. An angle greater than 90° but less than 180° is obtuse, and 127° falls in that range.
A: Reflex angles are between 180° and 360°, and 127° is below 180°.
B: A straight angle is exactly 180°, not 127°.
C (correct): 127° is greater than 90° and less than 180°, which is the obtuse range.
D: Acute angles are less than 90°, and 127° is larger than that.
Question 2 of 20 · easy
What is the complement of a 34° angle?
Show the answer
Answer: C
Correct answer: 56°. Complementary angles add to 90°, so the complement is
90 - 34 = 56
°.
A: This subtracts from 360°, the total around a point, not the 90° total for complements.
B: Complementary angles need not be equal; they only need to add up to 90°.
C (correct): Complementary angles total 90°, and 90 - 34 = 56.
D: This subtracts from 180°, which gives the supplement rather than the complement.
Question 3 of 20 · easy
A ray stands on a straight line, forming two angles. One of them measures 49°. What does the other angle measure?
Show the answer
Answer: D
Correct answer: 131°. Two adjacent angles whose outer sides form a straight line are a linear pair and add to 180°. So the other angle is
180 - 49 = 131
°.
A: This subtracts from 360°, which applies to angles all the way around a point.
B: This subtracts from 90°, but angles along a straight line total 180°.
C: The two angles of a linear pair are equal only when both are right angles.
D (correct): The two angles form a linear pair, so they total 180°: 180 - 49 = 131.
Question 4 of 20 · easy
Which statement correctly describes ray AB?
Show the answer
Answer: B
Correct answer: It begins at A and extends forever through B. A ray starts at an endpoint and goes on forever in one direction. In ray AB, A is the endpoint and the ray passes through B and continues.
A: Extending without end both ways describes line AB, not a ray.
B (correct): A ray has one endpoint, named first, and continues without end in the direction of the second point.
C: A measurable length belongs to segment AB; a ray never ends, so it has no length.
D: That describes ray BA, a different ray, because the endpoint is always named first.
Question 5 of 20 · easy
Four angles surround a point without overlapping. Three of them measure 140°, 85° and 60°. What is the measure of the fourth angle?
Show the answer
Answer: C
Correct answer: 75°. Angles around a point total 360°. The known angles add to
140 + 85 + 60 = 285
so the fourth angle is
360 - 285 = 75
°.
A: This comes from adding the known angles as 295° instead of 285°.
B: This comes from adding the known angles as 275° instead of 285°.
C (correct): The known angles total 285°, and 360 - 285 = 75.
D: This leaves the 60° angle out of the total and subtracts only 225° from 360°.
Question 6 of 20 · medium
Ray BD bisects angle ABC, and angle ABD measures 38°. Angle ABC forms a linear pair with angle CBE. What is the measure of angle CBE?
Show the answer
Answer: A
Correct answer: 104°. A bisector makes two equal halves, so angle ABC = 2(38) = 76°. A linear pair totals 180°, so angle CBE =
180 - 76 = 104
°.
A (correct): The whole angle ABC is 2(38) = 76°, and its linear-pair partner is 180 - 76 = 104.
B: This subtracts only the half angle, 38°, from 180° and forgets to double it first.
C: This subtracts 38 from 90, treating the pair as complementary instead of supplementary.
D: This is angle ABC itself; the question asks for its partner in the linear pair.
Question 7 of 20 · medium
Two parallel lines are cut by a transversal. A pair of corresponding angles measure (5x+12)∘ and (7x−20)∘. What is the measure of each of these angles?
Show the answer
Answer: B
Correct answer: 92°. Corresponding angles are equal when the lines are parallel:
5x + 12 = 7x - 20
Then 32 = 2x, so x = 16, and each angle is
5(16) + 12 = 92
°.
A: This is the supplement of the correct angle, not the corresponding angle itself.
B (correct): Setting 5x + 12 = 7x - 20 gives x = 16, and 5(16) + 12 = 92.
C: This is the value of x; the question asks for the angle measure.
D: This moves the -20 across without changing its sign, getting 2x = 8 and x = 4.
Question 8 of 20 · medium
Two parallel lines are cut by a transversal. One of a pair of same-side interior angles measures 118°. What does the other angle of that pair measure?
Show the answer
Answer: B
Correct answer: 62°. Between parallel lines, same-side interior angles add to 180°, so the other angle is
180 - 118 = 62
°.
A: This subtracts from 360°; same-side interior angles total 180°.
B (correct): Same-side interior angles between parallel lines are supplementary: 180 - 118 = 62.
C: This subtracts 90 from 118, which no angle relationship calls for.
D: This assumes same-side interior angles are equal, but they add to 180° instead.
Question 9 of 20 · medium
A transversal crosses two parallel lines. At the upper intersection the angles are numbered 1 (top left), 2 (top right), 3 (bottom left) and 4 (bottom right); angles 5, 6, 7 and 8 sit in the same positions at the lower intersection. If angle 2 measures 64°, what is the measure of angle 8?
Show the answer
Answer: D
Correct answer: 116°. Angles 2 and 6 are corresponding, so angle 6 = 64°. Angles 6 and 8 share a side along the lower parallel line and their outer sides lie along the transversal, so they form a linear pair and angle
8 = 180 - 64 = 116
°.
A: This treats angles 2 and 8 as equal, but they lie on the same side of the transversal and are not a matching pair.
B: This subtracts from 360°; angle 8 is one of the two angle sizes formed, 64° or 116°.
C: This subtracts 64 from 90, treating a supplementary relationship as complementary.
D (correct): Angle 6 corresponds to angle 2, so it is 64°, and angle 8 forms a linear pair with angle 6: 180 - 64 = 116.
Question 10 of 20 · medium
Two lines are cut by a transversal. Which observation is enough to prove that the two lines are parallel?
Show the answer
Answer: A
Correct answer: A pair of alternate interior angles both measure 74°. The converse tests need a relationship that holds only for parallel lines. Equal alternate interior angles meet that standard, while equal vertical angles and linear pairs totaling 180° occur with any crossing lines.
A (correct): Equal alternate interior angles are one of the converse tests that guarantee parallel lines.
B: Same-side interior angles must total 180° for parallel lines; 74 + 74 = 148 shows the lines are not parallel.
C: Vertical angles are equal for any two crossing lines, so this proves nothing about parallel lines.
D: Every linear pair totals 180°, whether or not the lines are parallel.
Question 11 of 20 · medium
Two complementary angles measure (3x+6)∘ and (2x−1)∘. What is the measure of the larger angle?
Show the answer
Answer: D
Correct answer: 57°. Complementary angles add to 90°:
(3x + 6) + (2x - 1) = 90
so
5x + 5 = 90
and x = 17. The angles are 57° and 33°, and the larger is 57°.
A: This is the value of x, not an angle measure.
B: This is the smaller angle, 2(17) - 1; the question asks for the larger one.
C: This sets the sum equal to 180°, treating the angles as supplementary, so x = 35.
D (correct): The sum 5x + 5 = 90 gives x = 17, so the angles are 57° and 33°.
Question 12 of 20 · medium
Three adjacent angles fill a straight line. They measure (3x)∘, (2x+10)∘ and 50°. What is the measure of the angle labeled (3x)∘?
Show the answer
Answer: A
Correct answer: 72°. Angles along a straight line add to 180°:
3x + (2x + 10) + 50 = 180
so
5x + 60 = 180
x = 24, and 3x = 72°. Check:
72 + 58 + 50 = 180
A (correct): The total 5x + 60 = 180 gives x = 24, so 3x = 72.
B: This sets the total to 360°, giving x = 60, but angles along a line total 180°.
C: This is the other unknown angle, 2(24) + 10.
D: This is x itself; the angle is three times that.
Question 13 of 20 · medium
The minute hand of a clock turns 6° each minute. Through how many degrees does it turn from 3:10 to 3:45?
Show the answer
Answer: A
Correct answer: 210°. From 3:10 to 3:45 is 35 minutes. At 6° per minute, the hand turns 35 times 6 = 210°.
A (correct): The time passed is 35 minutes, and 35 times 6° = 210°.
B: This multiplies 45 by 6, using the ending minute mark instead of the 35 minutes that passed.
C: This is the number of minutes, not the number of degrees turned.
D: This uses 3° per minute, half the actual rate of the minute hand.
Question 14 of 20 · medium
Ray OB lies between rays OA and OC, and angle AOC measures 112°. If angle AOB is (x+20)∘ and angle BOC is (2x+5)∘, what is the measure of angle BOC?
Show the answer
Answer: C
Correct answer: 63°. Adjacent angles add to the whole:
(x + 20) + (2x + 5) = 112
so
3x + 25 = 112
3x = 87 and x = 29. Then angle BOC =
2(29) + 5 = 63
°.
A: This is 180 - 112, treating angle AOC as part of a linear pair that the problem never describes.
B: This is angle AOB, 29 + 20, not angle BOC.
C (correct): The adjacent angles add to 112: 3x + 25 = 112, so x = 29 and 2(29) + 5 = 63.
D: This is x; the angle BOC is 2x + 5.
Question 15 of 20 · hard
A transversal crosses two parallel lines. At the upper intersection the angles are numbered 1 (top left), 2 (top right), 3 (bottom left) and 4 (bottom right); angles 5, 6, 7 and 8 sit in the same positions at the lower intersection. Angle 1 measures (4x+10)∘ and angle 7 measures (2x+20)∘. What is the measure of angle 6?
Show the answer
Answer: A
Correct answer: 70°. Same-side exterior angles are supplementary:
(4x + 10) + (2x + 20) = 180
so 6x = 150 and x = 25. Angle
7 = 2(25) + 20 = 70
°, and angle 6 is vertical to angle 7, so angle 6 = 70°.
A (correct): Angles 1 and 7 are same-side exterior, so 6x + 30 = 180 and x = 25; angle 7 is 70°, and angle 6 is vertical to it.
B: This is the value of x, not the measure of angle 6.
C: This is angle 1; angle 6 is not equal to angle 1 but supplementary to it.
D: This sets angles 1 and 7 equal, getting x = 5, but same-side exterior angles are supplementary.
Question 16 of 20 · hard
Ray OK bisects angle JOL, and each half measures (x+7)∘. Angle JOL forms a linear pair with an angle that measures (3x+6)∘. What is the measure of that partner angle?
Show the answer
Answer: C
Correct answer: 102°. The whole angle is
2(x + 7) = 2x + 14
A linear pair totals 180°:
2x + 14 + 3x + 6 = 180
so 5x = 160 and x = 32. The partner is
3(32) + 6 = 102
°; check:
78 + 102 = 180
A: This is angle JOL itself, not its partner in the linear pair.
B: This is one half of angle JOL, 32 + 7.
C (correct): The whole angle is 2x + 14, and (2x + 14) + (3x + 6) = 180 gives x = 32, so the partner is 3(32) + 6 = 102.
D: This is the value of x, not an angle measure.
Question 17 of 20 · hard
Five angles surround a point without overlapping. They measure x∘, (2x)∘, (3x)∘, 60° and 90°. What is the measure of the largest of the three unknown angles?
Show the answer
Answer: D
Correct answer: 105°. Angles around a point total 360°:
x + 2x + 3x + 60 + 90 = 360
So 6x = 210 and x = 35, making the unknown angles 35°, 70° and 105°. The largest is 105°.
A: This uses 180° as the total, giving x = 5, but angles around a point total 360°.
B: This is x, the smallest of the unknown angles.
C: This is 2x, the middle unknown angle, not the largest.
D (correct): The sum 6x + 150 = 360 gives x = 35, so 3x = 105.
Question 18 of 20 · hard
The supplement of an angle is 4 times the complement of the same angle. What is the measure of the angle?
Show the answer
Answer: D
Correct answer: 60°. Let the angle be x. Its supplement is 180 - x and its complement is 90 - x, so
180 - x = 4(90 - x) = 360 - 4x
Then 3x = 180 and x = 60°.
A: This sets the angle itself, not its supplement, equal to 4 times the complement: x = 4(90 - x).
B: This is the supplement of the angle, not the angle.
C: This is the complement of the angle, not the angle.
D (correct): With angle x, 180 - x = 4(90 - x) gives 3x = 180, so x = 60; check: 120 = 4(30).
Question 19 of 20 · hard
Two parallel lines are cut by a transversal. A pair of same-side interior angles measure (5x−15)∘ and (3x+35)∘. What is the measure of the angle that is vertical to the (3x+35)∘ angle?
Show the answer
Answer: B
Correct answer: 95°. Same-side interior angles are supplementary:
(5x - 15) + (3x + 35) = 180
so
8x + 20 = 180
and x = 20. Then
3(20) + 35 = 95
°, and vertical angles are equal, so the angle asked for is also 95°.
A: This sets the two same-side interior angles equal, getting x = 25, but they add to 180° instead.
B (correct): The pair is supplementary, so 8x + 20 = 180 and x = 20; the (3x + 35) angle is 95°, and its vertical angle equals it.
C: This is the value of x, not an angle measure.
D: This is the (5x - 15) angle, which is the supplement of the angle asked for.
Question 20 of 20 · hard
Two lines are cut by a transversal, forming alternate interior angles that measure (7x−20)∘ and (3x+40)∘. For what value of x are the two lines parallel?
Show the answer
Answer: B
Correct answer: 15. By the converse test, the lines are parallel when the alternate interior angles are equal:
7x - 20 = 3x + 40
Then 4x = 60 and x = 15, making both angles 85°.
A: This is the angle measure, 7(15) - 20; the question asks for x.
B (correct): Parallel lines need equal alternate interior angles: 7x - 20 = 3x + 40 gives 4x = 60 and x = 15.
C: This subtracts 20 from 40 instead of adding, getting 4x = 20.
D: This sets the angles to total 180, but alternate interior angles must be equal, not supplementary.
Which of these angle measures describes a reflex angle?
Show the answer
Answer: A
Correct answer: 205°. A reflex angle is greater than 180° but less than 360°. Of the measures listed, only 205° falls in that range.
A (correct): 205° is more than a straight angle (180°) and less than a full turn, so it is reflex.
B: 175° is less than 180°, so it is obtuse, not reflex.
C: Exactly 180° is a straight angle; a reflex angle must be larger than 180°.
D: 95° is between 90° and 180°, which makes it obtuse.
Practice 2 of 24 · medium
The complement of an angle measures 22°. What is the supplement of the same angle?
Show the answer
Answer: D
Correct answer: 112°. First find the angle:
90 - 22 = 68
°. Then find its supplement:
180 - 68 = 112
°. (Shortcut: the supplement is always 90° more than the complement.)
A: This subtracts 22 from 180, treating 22° as the angle itself instead of its complement.
B: 68° is the angle itself; the question asks for its supplement.
C: This subtracts 68 from 360, which finds the rest of a full turn, not a supplement.
D (correct): The angle is 90 - 22 = 68°, and its supplement is 180 - 68 = 112°.
Practice 3 of 24 · medium
Two straight lines cross. One of the four angles formed is 4 times as large as an angle next to it. What is the measure of the larger angle?
Show the answer
Answer: D
Correct answer: 144°. Neighboring angles at a crossing form a linear pair, so
x + 4x = 180
Then 5x = 180 and x = 36, so the larger angle is 4(36) = 144°.
A: 36° is the smaller angle; the question asks for the larger one.
B: This uses 90° instead of 180° for the pair (5x = 90 gives x = 18, 4x = 72), but neighbors on a line are supplementary.
C: Nothing says the lines are perpendicular; if the angles were 90° each, one could not be 4 times the other.
D (correct): Neighboring angles total 180°, so 5x = 180, x = 36, and 4x = 144°.
Practice 4 of 24 · medium
Picture two parallel lines crossed by a transversal. Number the four angles where it meets the upper line 1, 2, 3, 4, reading top-left, top-right, bottom-left, bottom-right, and number the four at the lower line 5 through 8 in that same order. Which angle corresponds to angle 3?
Show the answer
Answer: C
Correct answer: Angle 7. Corresponding angles sit in the same position at each intersection. Angle 3 is the bottom-left angle at the upper intersection, so its match is the bottom-left angle at the lower intersection, angle 7.
A: Angles 3 and 6 are alternate interior angles: both between the lines but on opposite sides of the transversal.
B: Angles 3 and 5 are same-side interior angles, which are supplementary rather than corresponding.
C (correct): Angle 7 is bottom left at the lower intersection, the same position angle 3 holds at the upper one.
D: Angle 2 is vertical to angle 3 at the same intersection, not a corresponding angle.
Practice 5 of 24 · medium
Lines AB and CD are perpendicular and meet at point E. Ray EF lies inside angle AEC and makes angle AEF measure 27°. What is the measure of angle FEC?
Show the answer
Answer: C
Correct answer: 63°. Perpendicular lines form 90° angles, so angle AEC = 90°. Angles AEF and FEC are adjacent and together make angle AEC, so angle FEC =
90 - 27 = 63
°.
A: This subtracts 27 from 180, but the two parts fill a right angle, not a straight line.
B: This adds 90 and 27 instead of subtracting the known part from the right angle.
C (correct): Angle AEC is a right angle, so the two adjacent parts total 90°: 90 - 27 = 63°.
D: Angle FEC would equal 27° only if EF bisected the right angle, and that is not given.
Practice 6 of 24 · easy
Two angles are supplementary, and one of them measures 76°. What does the other angle measure?
Show the answer
Answer: D
Correct answer: 104°. Supplementary angles add to 180°, so the other angle is
180 - 76 = 104
°.
A: 14° is the complement (90 - 76), not the supplement.
B: This subtracts from 360°, which applies to angles around a point, not to supplements.
C: An angle equal to 76° would be a vertical partner; supplements must add to 180°.
D (correct): 180 - 76 = 104°, so 76° and 104° are supplementary.
Practice 7 of 24 · hard
Parallel lines m and n are cut by transversal t, with m above n. The angles at line m are labeled 1 to 4 and those at line n are labeled 5 to 8, each time in the order upper-left, upper-right, lower-left, lower-right. Angle 2 measures (5x - 31)° and angle 7 measures (3x + 9)°. What is the measure of angle 4?
Show the answer
Answer: C
Correct answer: 111°. Angles 2 and 7 are alternate exterior angles, so they are equal:
5x - 31 = 3x + 9
giving 2x = 40 and x = 20. Angle
2 = 5(20) - 31 = 69
°.
Angle 1 forms a linear pair with angle 2, so angle
1 = 180 - 69 = 111
°, and angle 4 is vertical to angle 1, so angle 4 = 111°.
A: 69° is angle 2; angle 4 sits beside angle 2 on the line, so it is the supplement, not an equal angle.
B: 20 is the value of x, not the measure of an angle.
C (correct): Angle 2 is 69°; angle 4 is vertical to angle 1, which is the linear-pair partner of angle 2, so it is 180 - 69 = 111°.
D: This comes from a sign slip (2x = 31 - 9 gives x = 11, angle 2 = 24°); the correct step is 2x = 9 + 31.
Practice 8 of 24 · medium
Four adjacent angles fill one side of a straight line. They measure 25°, 41°, x° and (2x)°. What is the measure of the (2x)° angle?
Show the answer
Answer: D
Correct answer: 76°. Adjacent angles along a straight line total 180°:
25 + 41 + x + 2x = 180
so 3x = 114 and x = 38. The angle asked for is 2x = 76°.
A: 38 is x; the question asks for the angle labeled 2x.
B: This uses 360° instead of 180° (3x = 294), but angles along a line total 180°.
C: This uses 90° as the total (3x = 24), but the angles fill a straight line, which is 180°.
D (correct): 3x = 180 - 66 = 114, so x = 38 and 2x = 76°.
Practice 9 of 24 · medium
Two parallel lines are cut by a transversal. Two of the angles formed lie outside the parallel lines and on the same side of the transversal. If one of them measures 103°, what does the other measure?
Show the answer
Answer: C
Correct answer: 77°. Angles outside the parallel lines on the same side of the transversal are same-side exterior angles, and for parallel lines they are supplementary. The other angle is
180 - 103 = 77
°.
A: Same-side exterior angles are supplementary, not equal; it is alternate exterior angles that are equal.
B: This subtracts from 90°, but the pair must total 180°.
C (correct): Same-side exterior angles add to 180°, so the other angle is 180 - 103 = 77°.
D: This subtracts from 360°, which is the rule for angles around a point.
Practice 10 of 24 · easy
Two lines intersect, and one of the four angles formed measures 81°. What is the measure of the angle vertical to it?
Show the answer
Answer: C
Correct answer: 81°. Vertical angles sit directly across from each other at an intersection and are always equal, so the vertical angle also measures 81°.
A: 99° is the measure of each neighboring angle (180 - 81), not of the vertical angle.
B: 9° is the complement of 81°; vertical angles are equal, not complementary.
C (correct): Vertical angles are equal, so the angle across from 81° is also 81°.
D: 279° is what remains of a full turn after 81°, not the angle across from it.
Practice 11 of 24 · medium
An angle measures 18° more than twice its complement. What is the measure of the angle?
Show the answer
Answer: A
Correct answer: 66°. Let the complement be c, so the angle is 2c + 18. Together they make 90°:
c + 2c + 18 = 90
so 3c = 72 and c = 24. The angle is
2(24) + 18 = 66
°.
A (correct): With the complement c = 24°, the angle is 2(24) + 18 = 66°, and 66 + 24 = 90.
B: 24° is the complement; the question asks for the angle itself.
C: This sets the total at 180° (3c = 162, c = 54), which describes supplements, not complements.
D: 114° is the supplement of 66°; the question asks for the angle.
Practice 12 of 24 · medium
A transversal crosses two parallel lines and is not perpendicular to them. At the upper intersection the angles are numbered 1 (top left), 2 (top right), 3 (bottom left) and 4 (bottom right); angles 5, 6, 7 and 8 sit in the same positions at the lower intersection. Angle 1 measures 99°. Which of these angles must also measure 99°?
Show the answer
Answer: B
Correct answer: Angle 8. Angles 1 and 8 lie outside the parallel lines on opposite sides of the transversal, so they are alternate exterior angles and are equal. Angles 2, 3 and 7 each measure
180 - 99 = 81
°.
A: Angle 2 forms a linear pair with angle 1, so it measures 81°.
B (correct): Angles 1 and 8 are alternate exterior angles, which are equal when the lines are parallel.
C: Angle 3 is vertical to angle 2, so it also measures 81°.
D: Angles 1 and 7 are same-side exterior angles, so angle 7 is 180 - 99 = 81°.
Practice 13 of 24 · hard
Two lines intersect at point O. A pair of vertical angles measure (5x + 4)° and (7x - 20)°. A ray from O bisects one of the two other angles at the intersection. What is the measure of each half of that bisected angle?
Show the answer
Answer: A
Correct answer: 58°. Vertical angles are equal:
5x + 4 = 7x - 20
so 2x = 24 and x = 12, making each vertical angle 64°. The other two angles each form a linear pair with a 64° angle, so they measure
180 - 64 = 116
°. The bisector splits 116° into two halves of 58°.
A (correct): The neighboring angle is 180 - 64 = 116°, and the bisector cuts it into two 58° halves.
B: This halves the 64° angle, but the bisected angle is one of the other two angles, which measure 116°.
C: 116° is the whole angle being bisected; the question asks for each half.
D: 64° is the measure of each given vertical angle, not of a half of the neighboring angle.
Practice 14 of 24 · easy
Which of these figures has a length that can be measured?
Show the answer
Answer: D
Correct answer: A segment. A segment is the part of a line between two endpoints, so it has a definite, measurable length. Lines and rays go on forever, and a point has no size at all.
A: A line extends forever in both directions, so it has no measurable length.
B: A ray has one endpoint but continues forever in the other direction.
C: A point marks a location only and has no size.
D (correct): A segment stops at two endpoints, so its length can be measured.
Practice 15 of 24 · medium
A round tabletop is cut into four wedge-shaped pieces that meet at the center with no gaps or overlaps. The wedges' angles at the center are 105°, 80°, (3x)° and (2x + 5)°. What is the angle of the (2x + 5)° wedge?
Show the answer
Answer: B
Correct answer: 73°. Angles around a point total 360°:
105 + 80 + 3x + 2x + 5 = 360
so
5x + 190 = 360
5x = 170 and x = 34. The angle asked for is
2(34) + 5 = 73
°.
A: 34 is x; substitute it into 2x + 5 to get the angle.
B (correct): 5x = 170 gives x = 34, and 2(34) + 5 = 73°.
C: 102° is the (3x)° angle, not the one labeled (2x + 5)°.
D: 68 is 2x; the + 5 was left off when finding the angle.
Practice 16 of 24 · medium
Two lines are cut by a transversal. A pair of same-side interior angles measure 87° and 95°. What can you conclude about the two lines?
Show the answer
Answer: A
Correct answer: They are not parallel, because the two angles total 182° instead of 180°. If the lines were parallel, same-side interior angles would be supplementary. Here
87 + 95 = 182
°, not 180°, so the lines are not parallel.
A (correct): Same-side interior angles of parallel lines must add to exactly 180°, and these add to 182°.
B: Being close to 180° is not enough; the sum must be exactly 180° for the lines to be parallel.
C: The conclusion is right, but the reason is wrong: same-side interior angles of parallel lines are supplementary, not equal.
D: Linear pairs total 180° at any crossing, so this fact proves nothing about parallel lines.
Practice 17 of 24 · easy
In angle PQR, which point is the vertex?
Show the answer
Answer: C
Correct answer: Point Q. When an angle is named with three letters, the middle letter is the vertex. In angle PQR the middle letter is Q, and the sides pass through P and R.
A: P is a point on one side of the angle, not the vertex.
B: R is a point on the other side of the angle, not the vertex.
C (correct): The vertex is always the middle letter of a three-letter angle name.
D: The vertex is where the two sides meet, which is Q, not a point between P and R.
Practice 18 of 24 · hard
Two parallel rails are crossed by a straight cross-brace. Where the brace meets the upper rail, the angles are 1 and 2 above the rail and 3 and 4 below it, left to right; where it meets the lower rail, the angles are 5 and 6 above and 7 and 8 below, left to right. Angle 4 measures (8x - 14)° and angle 5 measures (5x + 31)°. What is the measure of angle 2?
Show the answer
Answer: B
Correct answer: 74°. Angles 4 and 5 lie between the rails on opposite sides of the brace, so they are alternate interior angles and are equal:
8x - 14 = 5x + 31
which gives 3x = 45 and x = 15. Angle
4 = 8(15) - 14 = 106
°.
Angle 2 sits directly above angle 4 on the same straight brace, so they form a linear pair: angle
2 = 180 - 106 = 74
°.
A: 106° is angle 4 (and angle 5); angle 2 forms a linear pair with angle 4, so it is supplementary, not equal.
B (correct): Angle 4 is 106°, and angle 2 is its linear-pair partner, so 180 - 106 = 74°.
C: 15 is x, not an angle measure.
D: This subtracts x from 180; the value of x must first be used to find an angle.
Practice 19 of 24 · easy
Angles R and S are complementary. If angle R measures 59°, what is the measure of angle S?
Show the answer
Answer: D
Correct answer: 31°. Complementary angles add to 90°, so angle
S = 90 - 59 = 31
°.
A: 121° is the supplement (180 - 59), not the complement.
B: This is an arithmetic slip; 59 + 41 = 100, not 90.
C: This subtracts from 360°, which is used for angles around a point.
D (correct): 90 - 59 = 31°, so 59° and 31° are complementary.
Practice 20 of 24 · medium
Through how many degrees does the minute hand of a clock turn in 40 minutes?
Show the answer
Answer: B
Correct answer: 240°. The minute hand makes a full 360° turn every 60 minutes, which is
360 / 60 = 6
° per minute. In 40 minutes it turns
40 × 6 = 240
°.
A: This treats 40 minutes as 40% of an hour; it is 40/60, or two-thirds, of an hour.
B (correct): At 6° per minute, 40 minutes gives 40 × 6 = 240°.
C: This uses 5° per minute, mixing up the 5 minutes between numbers with the degrees per minute.
D: This uses 3° per minute, which is half the actual rate.
Practice 21 of 24 · hard
A transversal crosses two parallel lines but is not perpendicular to them. One of the obtuse angles formed measures 40° less than three times one of the acute angles. What is the measure of the obtuse angle?
Show the answer
Answer: B
Correct answer: 125°. With parallel lines, every acute angle plus every obtuse angle totals 180°. Let the acute angle be a, so the obtuse angle is 3a - 40:
a + 3a - 40 = 180
giving 4a = 220 and a = 55. The obtuse angle is
3(55) - 40 = 125
°.
A: 55° is the acute angle; the question asks for the obtuse one.
B (correct): The acute angle is 55°, so the obtuse angle is 3(55) - 40 = 125°, and 55 + 125 = 180.
C: This drops the - 40 (4a = 180, a = 45, 3a = 135), ignoring part of the given relationship.
D: This sets the two angles equal, but an acute and an obtuse angle are supplementary, not equal.
Practice 22 of 24 · hard
Points A, O and B lie on a straight line. Ray OC is drawn above the line, and ray OD bisects angle COB. Angle AOC measures (2x + 8)° and angle COD measures (x + 16)°. What is the measure of angle AOD?
Show the answer
Answer: A
Correct answer: 129°. Because OD bisects angle COB, angle COB = 2(x + 16). Angles AOC and COB form a linear pair:
2x + 8 + 2x + 32 = 180
so 4x = 140 and x = 35.
Then angle AOC = 78° and angle COD = 51°, so angle AOD =
78 + 51 = 129
°.
A (correct): Angle AOD is angle AOC plus angle COD: 78 + 51 = 129°.
B: 51° is angle COD, only half of angle COB.
C: 102° is angle COB, the whole bisected angle, not angle AOD.
D: 35 is x, not an angle measure.
Practice 23 of 24 · hard
Three straight lines cross at a single point, forming six angles. Going around the point, three neighboring angles measure (x + 20)°, (2x + 15)° and (3x + 1)°, and the remaining three angles are their vertical angles. What is the measure of the largest angle?
Show the answer
Answer: A
Correct answer: 73°. Each of the three given angles has an equal vertical partner, so the three given angles fill half a turn:
(x + 20) + (2x + 15) + (3x + 1) = 180
then
6x + 36 = 180
6x = 144 and x = 24.
The angles are 44°, 63° and 73°, so the largest is 73°.
A (correct): With x = 24 the angles are 44°, 63° and 73°, which total 180°.
B: This sets the three angles equal to 360° (x = 54), forgetting that their vertical partners fill the other half of the turn.
C: 24 is x, not an angle measure.
D: 107° is the supplement of the largest angle, not the angle itself.
Practice 24 of 24 · medium
In a geometry figure that may not be drawn to scale, which marking tells you that two lines are parallel?
Show the answer
Answer: B
Correct answer: Matching arrowheads on the two lines. Parallel lines are marked with matching arrowheads. A small square means a right angle, and matching tick marks or arcs show equal segments or equal angles; appearance alone proves nothing.
A: A small square marks a 90° angle, which shows perpendicular lines, not parallel ones.
B (correct): Matching arrowheads are the standard mark for parallel lines.
C: Tick marks show that segments are equal in length, not that lines are parallel.
D: Figures may not be drawn to scale, so lines that look parallel are not proven parallel.
About this test
Every question has an explanation that names the relationship used, sets up the equation and checks the result. When a diagram could mislead you, the explanation says which facts are given and which only look true.
Use your score as a guide to targeted review. If transversal questions caused trouble, return to the sections on labeling the eight angles and the specific pair types. Algebra-based misses point to Solving Algebraic Angle Equations. You can also work the 24 extra practice questions for this lesson before continuing to triangles.
The same 124 lessons, 6,516 questions and 82 timed practice tests on your phone, plus flashcards with spaced review and progress tracking. Free to download, and it works offline.
ASVAB Camp
English ▾