JAMB Mathematics 2018 Paper

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