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In the diagram, ∠XWY congruent to ∠ZWY. Find XY.

In the diagram, ∠XWY congruent to ∠ZWY. Find XY.-example-1
User Nazneen
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1 Answer

9 votes

Answer:

10

Explanation:

Let XY = a

Since,

XY + YZ = XZ

a + YZ = 24

YZ = 24 - a

By angle bisector property:


(WX)/(WZ) = (XY)/(YZ) \\ \\ (15)/(21) = (a)/(24 - a) \\ \\ (5)/(7) = (a)/(24 - a) \\ \\ 5(24 - a) = 7a \\ \\ 120 - 5a = 7a \\ \\ 120 = 7a + 5a \\ \\ 120 = 12a \\ \\ a = (120)/(12) \\ \\ a = 10 \\ \\ \implies \: XY = 10

User Aaron Walerstein
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