Question

If AB || CD and XY is a transversal which meets AB at M & CD at N and also ∠AMX : ∠BMX = 3 : 2, then find ∠CNY.

Answer 1

Given $\angle 1:\angle 2=3:2$

$\therefore \angle 1=\frac{3}{5}\times 180={108}^{\circ }$ [1 Mark]

$\angle 5=\angle 1$ (corresponding angles)
$\angle 5+\angle 7={180}^{\circ }$ (linear pair)

Therefore, $\angle 7=\angle CNY={180}^{\circ }-{108}^{\circ }={72}^{\circ }$ [1 Mark]