Question

In figure, sides QP and RQ of $\Delta PQR$ are produced to points S and T respectively. If $\angle SPR={135}^o$ and $\angle PQT={110}^o$, find $\angle PRQ$.

• A. ${85}^o$
• B. ${65}^o$
• C. ${45}^o$
• D. ${35}^o$

Answer 1

The correct option is B ${65}^o$

Here, $\angle QPR+{135}^o={180}^o$ ....[Linear pair]

$\Rightarrow \angle QPR={45}^o$.

Now, $\angle QRP+\angle QPR=\angle PQT$ ....[Exterior angle property]

$\Rightarrow \angle QRP+{45}^o={110}^o$

$\Rightarrow \angle QRP={65}^o$.

Therefore, option $B$ is correct.