In the figure below, /MX/ = 8cm, /XN/ = 12cm, /NZ/ = 4cm and ∠ XMN = ∠ XZY. Calculate /YM/

In the figure below, /MX/ = 8cm, /XN/ = 12cm, /NZ/ = 4cm and ∠ XMN = ∠ XZY. Calculate /YM/

Answer Details

From the figure,
∠ XMN = ∠ XZY
Angle X is common
So, ∠ XNM = ∠ XYZ
Then from the angle relationship
$\frac{XM}{XZ}$ = $\frac{XN}{XY}$ = $\frac{MN}{ZY}$
XM = 8, XZ = 12 + 4 = 16,
XN = 12, XY = 8 + YM
$\frac{8}{16}$ = $\frac{12}{(8+YM)}$
Cross multiply
8(8 + YM) = 192
64 + 8YM = 192
8YM = 128
YM = $\frac{128}{8}$
= 16cm