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

Answer:

w=15

v=6

Step-by-step 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