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?
w =
(do not include the degree symbol in your answer.)

Explanation:

Step1: Alternate Interior Angles are Equal

Since alternate interior angles are equal when a transversal intersects two parallel lines, we have \(5v = 2w\). So, \(v=\frac{2w}{5}\).

Step2: Same - Side Exterior Angles are Supplementary

Same - side exterior angles are supplementary (their sum is \(180^{\circ}\)) when a transversal intersects two parallel lines. So, \(10w + 5v=180\).
Substitute \(v = \frac{2w}{5}\) into the equation \(10w+5v = 180\):
\(10w+5\times\frac{2w}{5}=180\)
Simplify the left - hand side: \(10w + 2w=180\)
Combine like terms: \(12w = 180\)

Step3: Solve for w

Divide both sides of the equation \(12w = 180\) by 12:
\(w=\frac{180}{12}=15\)

Answer:

\(15\)