Question

In the figure, $PR>PQ$ and $PS$ bisects $\angle QPR$. Then $\angle PSR>\angle PSQ$

• A. True
• B. False

Answer 1

The correct option is A True

In $\Delta PQR$

$PR>PQ$ (given)

$\Rightarrow \angle PQR>\angle PRQ$ (Since angle opposite to greater side is greater)

$\Rightarrow \angle PQR+\angle QPS>\angle PRQ+\angle RPS$ (since $\angle QPS=\angle RPS$)

$\Rightarrow -\left(\angle PQR+\angle QPS\right)<-\left(\angle PRQ+\angle RPS\right)$

$\Rightarrow 180-\left(\angle PQR+\angle QPS\right)<180-\left(\angle PRQ+\angle RPS\right)$

$\angle PSQ<\angle PSR$

$\Rightarrow \angle PSR>\angle PSQ$

Therefore it is true