Parallel Lines & Transversals Flashcards

A transversal cuts two parallel lines. One angle measures 70°. What is its alternate exterior angle?

Answer: 70°

Alternate exterior angles are congruent when lines are parallel, so the alternate exterior angle also measures 70°.

Lines l and m are parallel, cut by transversal t. One angle is (4x − 10)° and its corresponding angle is (2x + 40)°. Find x.

Answer: 25

Corresponding angles are equal: 4x − 10 = 2x + 40, so 2x = 50 and x = 25.

Which of the following does NOT prove that two lines cut by a transversal are parallel?

Answer: Corresponding angles are supplementary

Corresponding angles must be equal (not supplementary) to prove lines are parallel; supplementary corresponding angles do not guarantee parallelism.

If a transversal is perpendicular to one of two parallel lines, it is _____ perpendicular to the other.

Answer: always

Because corresponding angles are equal for parallel lines, a 90° angle at one intersection means a 90° angle at the other — the transversal is always perpendicular to both.

Two parallel lines are cut by a transversal. One co-interior angle is 3 times the other. Find the smaller angle.

Answer: 45°

Let the smaller angle be x; then x + 3x = 180°, so 4x = 180° and x = 45°.

A transversal creates a 55° angle with line l. If l ∥ m, what is the co-interior angle on the same side with line m?

Answer: 125°

Co-interior angles are supplementary, so the angle with line m is 180° − 55° = 125°.

What is the total number of angles formed when a single transversal intersects two distinct lines?

Answer: 8

A transversal creates 4 angles at each of the 2 intersection points, giving 4 × 2 = 8 angles in total.