Point Y is in the interior of ∠XWZ. Given that WX and WZ are opposite rays and m∠XWY=​4(m∠​YWZ), what is m∠​YWZ?

Answer 1

Opposite rays form a line so the two angles add up to 180, divide 180 by 5 to get the smaller angle.

smaller angle = 36

larger angle = 144

one angle is 4 times the other angle:

first angle is x

second angle is 4x

add them you get

5x = 180

Answer 2

Let N = angle WXZ

then 4x+x = N

5x = N

x = N/5 is the smaller interior angle

and

(4N)/5 is the larger interior angle