Question

A transversal intersects two parallel lines. The measures of a pair of alternate interior angles are 5v and​ 2w. The measures of a pair of​ same-side exterior angles are 10w and 5v. What are the values of w and​ v?A transversal intersects two parallel lines. The measures of a pair of alternate interior angles are 5v and​ 2w. The measures of a pair of​ same-side exterior angles are 10w and 5v. What are the values of w and​ v?

Answer 1

w=15

v=6

Explanation:

Interior Angle Theroum , we can write

5 v = 2 w (1)

The measures of a pair of​ same-side exterior angles are supplementary

10 w + 5 v= 180 (2)

substitute 1 from 2

10 w + 2 w = 180

12 w = 180

w=180/12

w=15

The measures of a pair of alternate interior angles are

5 v=2 w

5 v=2(15)

5 v=30

v=30/5

v=6