← Back to the Parallel Lines Transversal Angles test
Last updated: October 22, 2026 · Written by the Math Made Easy math teachers
Standards: G-CO.C.9 · Level: Grade 10 Geometry
Question 1 Name the pairs (2 points)
- Alternate interior angles.
- Alternate exterior angles.
(a) alternate interior, (b) alternate exterior
Scoring: 1 point per correct name.
Question 2 Find three angles (3 points)
- ∠2 and ∠6 are corresponding: 61°.
- ∠4 and ∠2 form a linear pair: 180° − 61° = 119°.
- ∠7 is vertical to ∠6, so it equals 61°.
(a) 61°, (b) 119°, (c) 61°
Scoring: 1 point per angle.
Question 3 Alternate interior equation (2 points)
Alternate interior angles are equal: 4x + 11 = 6x − 19, so 30 = 2x and x = 15. Each angle is 4(15) + 11 = 71°, and 6(15) − 19 = 71°.
x = 15; 71°
Scoring: 1 point for x, 1 point for the measure.
Question 4 Decide if lines are parallel (3 points)
- Parallel: congruent corresponding angles.
- Not parallel: 64° ≠ 66°, so the alternate interior angles are not congruent.
- Parallel: 105° + 75° = 180°, so the same-side interior angles are supplementary.
(a) parallel, (b) not parallel, (c) parallel
Scoring: 1 point per part (answer and reason).
Question 5 Parallel with same-side angles (2 points)
The angles must be supplementary: 7x + 4 + 5x + 20 = 180, so 12x + 24 = 180 and x = 13. The angles are 7(13) + 4 = 95° and 5(13) + 20 = 85°.
x = 13; 95° and 85°
Scoring: 1 point for x, 1 point for both angles.
Question 6 Prove lines parallel (3 points)
| Statement | Reason |
|---|---|
| 1. ∠2 ≅ ∠7 | Given |
| 2. ∠7 ≅ ∠6 | Vertical angles are congruent |
| 3. ∠2 ≅ ∠6 | Transitive Property of congruence |
| 4. a ∥ b | Converse of the Corresponding Angles Theorem |
Scoring: 1 point for statements 2 and 3 with reasons, 1 point for the conclusion, 1 point for correct order.
Question 7 Equidistant point (3 points)
- 2x + 9 = 4x − 7, so 16 = 2x and x = 8.
- PA = 2(8) + 9 = 25.
- The midpoint is 24 from each end and the bisector is perpendicular to AB, so the distance is √(25² − 24²) = √49 = 7.
x = 8; PA = 25; distance 7
Scoring: 1 point per part.
Question 8 Crossing bike lanes (2 points)
The matching (corresponding) angle on the second lane is also 38°. An angle on the same side between the lanes is supplementary to 38°, so it measures 180° − 38° = 142°.
38° and 142°
Scoring: 1 point for each angle with a valid reason.