MATH SOLVE

5 months ago

Q:
# 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?

Accepted Solution

A:

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

[tex](11x-19)+(8x+28)=180[/tex]

We combine our like terms (the x's get combined, then the constants get combined) and have:

[tex]19x+9=180[/tex]

Cancel the 9 first by subtraction:

[tex]19x+9-9=180-9 \\ 19x=171[/tex]

Cancel the 19 by division:

[tex] \frac{19x}{19}= \frac{171}{19} \\ x=9[/tex]

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°

[tex](11x-19)+(8x+28)=180[/tex]

We combine our like terms (the x's get combined, then the constants get combined) and have:

[tex]19x+9=180[/tex]

Cancel the 9 first by subtraction:

[tex]19x+9-9=180-9 \\ 19x=171[/tex]

Cancel the 19 by division:

[tex] \frac{19x}{19}= \frac{171}{19} \\ x=9[/tex]

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°