Transversal of Parallel Lines Worksheet

Transversal of Parallel Lines

Read each question carefully and answer to the best of your ability. Show all your work for full credit.

1. In the diagram below, lines 'a' and 'b' are parallel, and line 't' is a transversal. If ∠1 = 110°, what is the measure of ∠5?

2. Which of the following angle pairs are always congruent when a transversal intersects two parallel lines?

3. When two parallel lines are intersected by a transversal, corresponding angles are  .

4. Consecutive interior angles are   when a transversal intersects two parallel lines.

5. Alternate exterior angles are   when a transversal intersects two parallel lines.

6. Given that line 'm' is parallel to line 'n', and a transversal 'p' intersects them. If one pair of alternate interior angles measures (3x + 15)° and (5x - 25)°, find the value of x and the measure of each angle.

7. Explain the relationship between corresponding angles and alternate interior angles when parallel lines are cut by a transversal.

8. If two lines are cut by a transversal and the alternate exterior angles are supplementary, then the lines are parallel.

9. Vertical angles are always congruent, regardless of whether the lines are parallel.

10. In the figure below, lines j and k are parallel. If m∠2 = (6x - 20)° and m∠7 = (4x + 10)°, find the value of x and the measure of all eight angles formed by the transversal. Justify each step of your solution.