Question

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

Answer 1

Answer:

10

Step-by-step explanation:

Let XY = a

Since,

XY + YZ = XZ

a + YZ = 24

YZ = 24 - a

By angle bisector property:

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