Question

State True or False.

In figure, $\angle PQR=\angle PRQ$, then $\angle PQS=\angle PRT$.

• A. True
• B. False

Answer 1

The correct option is A True

Let $\angle PQR=\angle PRQ=x$ (say).....(1)
Now, $\angle PQS+\angle PQR={180}^o$ [Linear pair of angles]
and $\angle PRT+\angle PRQ={180}^o$ [Linear pair of angles]
$\Rightarrow \angle PQS+\angle PQR=\angle PRT+\angle PRQ[\because each={180}^o]$
$\Rightarrow \angle PQS+x=\angle PRT+x$ [By (1)]
$\Rightarrow \angle PQS=\angle PRT$.

Hence, the statement is true and option $A$ is correct.