JAMB 1983 · UME · Q19

In the figure, $FGHK$ is a rhombus and $\angle GKF = 30^\circ$ . What is the value of the angle $x$ at $H$ ?

Worked solution (try it first)

A diagonal of a rhombus bisects the angles it passes through.
$KG$ bisects $\angle HKF$ , so $\angle HKF = 2 \times 30^\circ = 60^\circ$ .
$KF \parallel HG$ , so the angles at $K$ and $H$ are co-interior and add up to $180^\circ$ .
So $x = 180^\circ - 60^\circ = 120^\circ$ , option D.