JAMB 2003 · UME · Q25

In the diagram, $PQ$ is parallel to $RS$ . What is the value of $\alpha + \beta + \gamma$ ?

Worked solution (try it first)

Draw a line through the apex parallel to $PQ$ and $RS$ .
It splits $\beta$ into two parts.
$\alpha$ and the left part of $\beta$ are co-interior angles between $PQ$ and the new line, so they add up to $180^\circ$ .
In the same way $\gamma$ and the right part of $\beta$ add up to $180^\circ$ .
So $\alpha + \beta + \gamma = 180^\circ + 180^\circ$
$= 360^\circ$ , option D.