# Question content area top Part 1 Point Y is in the interior of XWZ. Given that and are opposite rays and mXWY​4(m​YWZ)

Question

Question content area top
Part 1
Point Y is in the interior of XWZ. Given that and are opposite rays and mXWY​4(m​YWZ), what is m​YWZ?

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1 week 2023-01-24T17:37:33+00:00 1 Answer 0 views 0

1. The missing angle in the question is; m∠YWZ = 36°

### How to find unknown angles?

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°