JAMB 1984 · UME · Q32

In the figure, $PQRSTW$ is a regular hexagon and $QS$ intersects $RT$ at $V$ . Calculate $\angle TVS$ .

Worked solution (try it first)

Each interior angle of a regular hexagon is $120^\circ$ .
Triangle $QRS$ is isosceles ( $QR = RS$ ), so $\angle RSQ = \frac{180^\circ - 120^\circ}{2}$
$= 30^\circ$ .
In the same way triangle $RST$ is isosceles ( $RS = ST$ ), so $\angle SRT = 30^\circ$ .
$\angle TVS$ is an exterior angle of triangle $VRS$ , so it equals the sum of the two opposite interior angles: $30^\circ + 30^\circ = 60^\circ$ , option A.