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 wand v?

Answer 1

The value of v is 6° and the value of w is 15°

Explanation:

we know that

When parallel lines are cut by a transversal line, the same-side exterior angles are supplementary and each pair of alternate interior angles is equal in measure

so

5v=2w -----> equation A

10w+5v=180 ----> equation B

substitute equation A in equation B and solve for w

10w+(2w)=180

12w=180

w=15°

Find the value of v

5v=2w -----> v=2w/5

v=2(15)/5=6°

therefore

The value of v is 6° and the value of w is 15°