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

Mathematics

1 answer:

EleoNora [17]3 years ago

5 0

Answer:

m∠YWZ=36°

Step-by-step explanation:

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 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\angle YWZ=180°

5(m∠YWZ)=180°

m∠YWZ=36°

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Step-by-step explanation:

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