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: Use alternate - interior angles property

When a transversal intersects two parallel lines, alternate - interior angles are congruent. So, we set up the equation $5v = 2w$.

Step2: Use same - side exterior angles property

When a transversal intersects two parallel lines, same - side exterior angles are supplementary. So, $10w+5v = 180$.

Step3: Substitute $5v$ in the second equation

Since $5v = 2w$, substitute $5v$ in $10w + 5v=180$ with $2w$. We get $10w+2w=180$.

Step4: Solve for $w$

Combine like terms: $12w = 180$. Then, divide both sides by 12: $w=\frac{180}{12}=15$.

Step5: Solve for $v$

Substitute $w = 15$ into the equation $5v = 2w$. So, $5v=2\times15$, which gives $5v = 30$. Divide both sides by 5, and $v = 6$.

Answer:

$w = 15$
$v = 6$