Parallel Lines Angles Quiz � Master Angle Relationships (8.G.A.5)

1) If ∠x = 78° and it is a corresponding angle, what is the measure of its partner angle?

102°

78°

90°

180°

Corresponding angles are equal.

So, partner corresponding angle = 78°.

Explanation

Corresponding angles are equal.

So, partner corresponding angle = 78°.

2) If ∠1 = 65° on a parallel line diagram, what is the measure of the corresponding angle?

25°

65°

115°

180°

Corresponding angles on parallel lines are equal. So, the corresponding angle = 65°.

Explanation

Corresponding angles on parallel lines are equal. So, the corresponding angle = 65°.

3) In the diagram, ∠x = 120°. What is the measure of the corresponding angle?

60°

120°

150°

180°

Corresponding angles are equal.

So, corresponding angle = 120°.

Explanation

Corresponding angles are equal.

So, corresponding angle = 120°.

4) In a parallel-line diagram, one angle is 45°. What is the measure of its alternate exterior angle?

45°

90°

135°

180°

Alternate exterior angles are equal, so angle = 45°

Explanation

Alternate exterior angles are equal, so angle = 45°

5) If an angle measures 150°, what is the measure of its alternate exterior angle?

30°

60°

120°

150°

Alternate exterior angles are equal.

So, alternate exterior angle = 150°.

Explanation

Alternate exterior angles are equal.

So, alternate exterior angle = 150°.

6) Two parallel lines are cut by a transversal. If an exterior angle is 120°, what is the measure of the alternate interior angle?

60°

90°

120°

180°

Alternate interior angles are equal. Opposite side angle = 120°.

Explanation

Alternate interior angles are equal. Opposite side angle = 120°.

7) In a parallel-line diagram, ∠1 = 132°. What is the measure of the alternate interior angle?

42°

48°

132°

138°

Alternate interior angles are equal.

So, alternate interior angle = 132°.

Explanation

Alternate interior angles are equal.

So, alternate interior angle = 132°.

8) If two parallel lines are cut with a transversal, which type of angle pairs are always supplementary?

Vertical angles

Alternate interior angles

Consecutive interior angles

Corresponding angles

Same-side (consecutive) interior angles sum to 180°.

So, consecutive interior angles are supplementary.

Explanation

Same-side (consecutive) interior angles sum to 180°.

So, consecutive interior angles are supplementary.

9) Two parallel lines are cut by a transversal. If one angle is 70°, what is its vertical angle?

20°

70°

110°

180°

Vertical angles are equal. Opposite angle to 70° = 70°.

Explanation

Vertical angles are equal. Opposite angle to 70° = 70°.

10) A transversal cuts two parallel lines. ∠1 = 85°. Which other angle also equals 85°?

Alternate exterior angle

Consecutive interior angle

Linear pair angle

Supplementary angle

Angles equal to 85° include corresponding, alternate interior, alternate exterior, and vertical. Among choices, only alternate exterior matches.

So, alternate exterior angle = 85°.

Explanation

Angles equal to 85° include corresponding, alternate interior, alternate exterior, and vertical. Among choices, only alternate exterior matches.

So, alternate exterior angle = 85°.

11) In a parallel-line setup, ∠1 = 63°. Which angle is also 63°?

Alternate interior angle

Consecutive interior angle

Linear pair angle

Supplementary angle

Alternate interior angles are equal.

So, alternate interior angle = 63°.

Explanation

Alternate interior angles are equal.

So, alternate interior angle = 63°.

12) If ∠a = 115° in a parallel line and transversal setup, what is the measure of the consecutive (same-side) interior angle?

55°

65°

115°

125°

Same-side interior angles are supplementary. 115° + angle = 180°.

So, angle = 180° − 115° = 65°.

The consecutive interior angle is 65°

Explanation

Same-side interior angles are supplementary. 115° + angle = 180°.

So, angle = 180° − 115° = 65°.

The consecutive interior angle is 65°

13) A transversal creates ∠a = 118°. What is the measure of the linear pair angle next to it?

52°

62°

72°

82°

Linear pairs are supplementary. 118° + angle = 180°.

So, the linear pair angle is 62°.

Explanation

Linear pairs are supplementary. 118° + angle = 180°.

So, the linear pair angle is 62°.

14) If ∠x = 100°, what is the measure of its consecutive interior angle?

80°

90°

100°

120°

Same-side interior angles are supplementary. 100° + angle = 180°.

So, the consecutive interior angle is 80°.

Explanation

Same-side interior angles are supplementary. 100° + angle = 180°.

So, the consecutive interior angle is 80°.

15) If one angle formed by a transversal is 40°, what is the measure of the linear pair angle next to it?

40°

50°

90°

140°

Linear pair angles sum to 180°: 180 − 40 = 140°.

Explanation

Linear pair angles sum to 180°: 180 − 40 = 140°.

16) If ∠m and ∠n are consecutive interior angles and ∠m = 75°, what is ∠n?

75°

95°

105°

115°

Consecutive interior angles are supplementary: 180 − 75 = 105°.

Explanation

Consecutive interior angles are supplementary: 180 − 75 = 105°.

17) Which of the following statements is false about angles formed by parallel lines and a transversal?

Vertical angles are always congruent.

Corresponding angles are congruent if lines are parallel.

Alternate interior angles are congruent if lines are parallel.

Consecutive interior angles are congruent if lines are parallel.

Consecutive interior angles are supplementary, not congruent.

So, “Consecutive interior angles are congruent” is false.

Explanation

Consecutive interior angles are supplementary, not congruent.

So, “Consecutive interior angles are congruent” is false.

18) If ∠m = 90° in a parallel-line setup, what is true about the transversal?

It must be perpendicular to the parallel lines.

It creates only acute angles.

It creates only obtuse angles.

It makes corresponding angles supplementary.

If one angle is 90° and lines are parallel, the transversal is perpendicular to both.

Explanation

If one angle is 90° and lines are parallel, the transversal is perpendicular to both.

19) If two lines are parallel and cut by a transversal, which statement is true?

Alternate interior angles are complementary.

Corresponding angles are equal.

Vertical angles are always 90°.

All interior angles are supplementary.

On parallel lines, corresponding angles always match in measure.

Explanation

On parallel lines, corresponding angles always match in measure.

20) Two parallel lines are cut by a transversal. If one angle is 55°, which of the following is also 55°?

Alternate interior angle

Corresponding angle

Vertical angle

All of the above

Vertical, corresponding, and alternate interior angles are all equal to the given angle in parallel lines.

So, all listed angle types equal 55°.

Explanation

Vertical, corresponding, and alternate interior angles are all equal to the given angle in parallel lines.

So, all listed angle types equal 55°.

Angles Formed by Parallel Lines and a Transversal Quiz

1) If ∠x = 78° and it is a corresponding angle, what is the measure of its partner angle?

2) If ∠1 = 65° on a parallel line diagram, what is the measure of the corresponding angle?

3) In the diagram, ∠x = 120°. What is the measure of the corresponding angle?

4) In a parallel-line diagram, one angle is 45°. What is the measure of its alternate exterior angle?

5) If an angle measures 150°, what is the measure of its alternate exterior angle?

6) Two parallel lines are cut by a transversal. If an exterior angle is 120°, what is the measure of the alternate interior angle?

7) In a parallel-line diagram, ∠1 = 132°. What is the measure of the alternate interior angle?

8) If two parallel lines are cut with a transversal, which type of angle pairs are always supplementary?

9) Two parallel lines are cut by a transversal. If one angle is 70°, what is its vertical angle?

10) A transversal cuts two parallel lines. ∠1 = 85°. Which other angle also equals 85°?

11) In a parallel-line setup, ∠1 = 63°. Which angle is also 63°?

12) If ∠a = 115° in a parallel line and transversal setup, what is the measure of the consecutive (same-side) interior angle?

13) A transversal creates ∠a = 118°. What is the measure of the linear pair angle next to it?

14) If ∠x = 100°, what is the measure of its consecutive interior angle?

15) If one angle formed by a transversal is 40°, what is the measure of the linear pair angle next to it?

16) If ∠m and ∠n are consecutive interior angles and ∠m = 75°, what is ∠n?

17) Which of the following statements is false about angles formed by parallel lines and a transversal?

18) If ∠m = 90° in a parallel-line setup, what is true about the transversal?

19) If two lines are parallel and cut by a transversal, which statement is true?

20) Two parallel lines are cut by a transversal. If one angle is 55°, which of the following is also 55°?