Question

In $\Delta PQR,PQ=PR,\angle QPR$ is equal to:

• A. ${20}^o$
• B. ${30}^o$
• C. ${40}^o$
• D. ${50}^o$

Answer 1

Answer: (A)

${20}^o$

Given, in $△PQR,PQ=PR$

Therefore, $△PQR$ is an isosceles triangle with equal base angles, $\angle Q=\angle R$.

Exterior $\angle R={100}^o$

Therefore, $PRQ={80}^o$

As angles $Q$ and $R$ are equal, $\angle PQR={80}^o$

$\angle P+\angle Q+\angle R={180}^o$

$\therefore \angle P={20}^o$ i.e. $\angle QPR={20}^o$