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?

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Mathematics

20 June, 03:43

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?

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Francesca Hebert · Answer 1

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