Question

In a $\Delta PQR$, if $PQ=PR$ and $\angle Q$ is twice that of $\angle P$, then $\angle Q=$

• A. ${72}^{\circ }$
• B. ${36}^{\circ }$
• C. ${144}^{\circ }$
• D. ${108}^{\circ }$

Answer 1

Answer: (A)

${72}^{\circ }$

Given, $PQ=PR$
$\Rightarrow \angle Q=\angle R$
Also given $\angle Q=2\angle P$
We have
$\angle P+\angle Q+\angle R={180}^{\circ }$
$\frac{\angle Q}{2}+\angle Q+\angle Q={180}^{\circ }$
$\frac{5}{2}\angle Q={180}^{\circ }$
$\angle Q={72}^{\circ }$