Question

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

Answer 1

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`