Geometry Parallel Lines & Transversals 2 — Questions and Answers
Question 1: Parallel lines l and m are cut by a transversal. One alternate interior angle measures 65°. What does the other alternate interior angle measure?
- 115°
- 55°
- 65° (Correct answer)
- 25°
Correct answer: 65°
Alternate interior angles are congruent when lines are parallel, so both measure 65°.
Question 2: Which angle relationship, when congruent, proves that two lines cut by a transversal are parallel?
- Supplementary angles
- Co-interior angles
- Complementary angles
- Corresponding angles (Correct answer)
Correct answer: Corresponding angles
If corresponding angles are equal, the lines are parallel by the Converse of the Corresponding Angles Postulate.
Question 3: When a transversal crosses two parallel lines (not at 90°), how many distinct angle measures are formed among the 8 angles?
- 8
- 4
- 1
- 2 (Correct answer)
Correct answer: 2
Due to parallel line properties, all 8 angles take only 2 distinct values — one angle and its supplement.
Question 4: Consecutive interior angles formed by two parallel lines and a transversal are also known as _____.
- alternate interior angles
- co-interior angles (Correct answer)
- vertical angles
- corresponding angles
Correct answer: co-interior angles
Consecutive interior angles (same-side interior angles) are also called co-interior angles.
Question 5: Two parallel lines are cut by a transversal forming co-interior angles of 3x° and (2x + 10)°. What is x?
- 30
- 36
- 34 (Correct answer)
- 40
Correct answer: 34
Co-interior angles sum to 180°: 3x + 2x + 10 = 180, so 5x = 170 and x = 34.
Question 6: Line l is parallel to line m. A transversal creates an angle of 72° with line l. What is the corresponding angle with line m?
- 108°
- 18°
- 36°
- 72° (Correct answer)
Correct answer: 72°
Corresponding angles are congruent when lines are parallel, so the angle with line m is also 72°.
Question 7: Two parallel lines are cut by a transversal. One of the eight angles measures 40°. How many of the eight angles measure 140°?
- 1
- 2
- 3
- 4 (Correct answer)
Correct answer: 4
The 8 angles consist of two distinct measures: 40° and its supplement 140°. Exactly four angles measure each value.
Geometry Parallel Lines & Transversals 2
Parallel lines l and m are cut by a transversal.
One alternate interior angle measures 65°.
What does the other alternate interior angle measure?