Question

In Fig, sides $ QP$and $ RQ$of $ △PQR$ are produced to points $ S$and $ T$ respectively. If $ SPR=135°$and $ \angle PQT=110°,$find $ \angle PRQ.$

Answer 1

Step 1:Solve for the value of $\angle PQR.$

$\angle TQP=110°,\angle SPR=135°$

$TQR$is a straight line (from figure)

As studied, $TQP$ and $PQR$ will form a linear pair.

$\angle TQP+\angle PQR=180°$

$\Rightarrow 110+\angle PQR=180$

$\Rightarrow \angle PQR=70°$

Step 2:Solve for the value of $\angle PRQ.$

In $△PQR,$ $QP$is extended to $S$ so,$\angle SPR$ forms the exterior angle.

Thus, $\angle SPR$ is equal to the sum of interior opposite angles. (Exterior angle property)

$\Rightarrow \angle PQR+\angle PRQ=135°$

$$\begin{gathered} \Rightarrow 70+\angle PRQ=135 \\ \Rightarrow \angle PRQ=135-70 \\ =65° \end{gathered}$$

Hence the value of $\angle PRQ=65°.$