Question

A transversal interersects 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 (consecutive exterior) are 10w and 5v. What are the values of w and v?

Answer 1

Answer:
`v=6, w=15`

Explanation:

The pair of alternate interior angles are congruent, so
`5v=2w \implies 10w=25v`.

The consecutive exterior angles are supplementary, so

`10w+5v=180\\\\25v+5v=180\\\\\\30v=180\\\\v=6\\\\\implies w=2.5(6)=15`