Question

part 1 of 2
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?

Explanation:

Step1: Recall angle properties

When a transversal intersects two parallel lines, alternate interior angles are equal, and same - side exterior angles are supplementary (their sum is \(180^{\circ}\)). So we have two equations:

1. From alternate interior angles: \(5v = 2w\) (Equation 1)
2. From same - side exterior angles: \(10w+5v=180\) (Equation 2)

Step2: Substitute Equation 1 into Equation 2

Substitute \(5v = 2w\) into \(10w + 5v=180\). We get \(10w+2w = 180\).
Combine like terms: \(12w=180\).

Step3: Solve for \(w\)

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

Step4: Solve for \(v\)

Substitute \(w = 15\) into Equation 1 (\(5v=2w\)). So \(5v=2\times15 = 30\).
Divide both sides by 5: \(v=\frac{30}{5}=6\).

Answer:

\(w = 15\), \(v=6\)