JAMB 1986 · UME · Q43

In the figure, $PQ \parallel ST$ and $RS \parallel UV$ . If $\angle PQR = 35^\circ$ and $\angle QRS = 65^\circ$ , find $\angle STV$ .

Worked solution (try it first)

Produce $SR$ back beyond $R$ to meet $PQ$ at a point $X$ .
Angles on a straight line: $\angle XRQ = 180^\circ - 65^\circ$
$= 115^\circ$ .
The angles of triangle $XQR$ add up to $180^\circ$ , so $\angle QXR = 180^\circ - 115^\circ - 35^\circ$
$= 30^\circ$ .
This is the angle between the lines $PQ$ and $RS$ .
$ST \parallel PQ$ and $TV \parallel RS$ , so $\angle STV$ is the same angle between the same two directions: $\angle STV = 30^\circ$ , option A.