Question

1. mathematical connections 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 - relationships

When a transversal intersects two parallel lines, alternate - interior angles are congruent and same - side exterior angles are supplementary.
Since alternate - interior angles are congruent, we have $5v = 2w$.
Since same - side exterior angles are supplementary, we have $10w+5v = 180$.

Step2: Substitute $5v$ in the second equation

Substitute $5v$ with $2w$ in the equation $10w + 5v=180$. We get $10w+2w = 180$.
Combining like terms, $12w=180$.
Dividing both sides by 12, we find $w=\frac{180}{12}=15$.

Step3: Find the value of $v$

Substitute $w = 15$ into the equation $5v = 2w$.
We have $5v=2\times15$.
$5v = 30$.
Dividing both sides by 5, we get $v = 6$.

Answer:

$w = 15$, $v = 6$