Question

In the figure, WY¯¯¯¯¯¯¯¯¯WY¯ and XZ¯¯¯¯¯¯¯¯XZ¯ intersect at point VV, the measure of ∠WVZ∠WVZ is (11x−19)°(11x−19)°, and the measure of ∠WVX∠WVX is (8x+28)°(8x+28)°.
What is the measure of ∠YVZ∠YVZ?

Answer 1

Assuming a diagram similar to the one I've attached, ∠YVZ is a vertical angle to ∠WVX, which means they have an equal measure.  Additionally, ∠WVZ and ∠WVX form a linear pair, which means they are supplementary (sum to 180°).  That means we start out with the equation
$(11x-19)+(8x+28)=180$
We combine our like terms (the x's get combined, then the constants get combined) and have:
$19x+9=180$
Cancel the 9 first by subtraction:
$19x+9-9=180-9 \\ 19x=171$
Cancel the 19 by division:
$\frac{19x}{19}= \frac{171}{19} \\ x=9$
Since we know that our angle we're looking for, ∠YVZ, is the same measure as ∠WVX, we substitute 9 in for x:
8(9)+28=72+28=100°