The missing angle in the question is; m∠YWZ = 36°
Opposite rays are two rays that both start from a common point and go off in exactly opposite directions. Because of this the two rays (WX and WZ) form a single straight line through the common endpoint W.
If rays WX and WZ are opposite, then angle XWZ is a straight angle. A straight angle always has the measure of 180°.
Point Y is in the interior of ∠XWZ, then angles XWY and EWZ are supplementary angles (together form straight angle XWZ). Supplementary angles always add up to 180°, then
m∠XWY+m∠YWZ=180°
You are given that
m∠XWY = 4(m∠YWZ).
Substitute it into the previous equality:
4(m∠YWZ) + m∠YWZ=180°
5(m∠YWZ) = 180°
m∠YWZ = 36°
Read more about unknown angles at; https://brainly.com/question/14936289
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