Question

In a $\Delta$ $PQR$, $PQ$ $=$ $PR$ and $\angle$ $Q$ is twice that of $\angle$ $P$. Then $\angle$Q$=$____________.

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

Answer 1

The correct option is A ${72}^o$

In a $\Delta PQR$, we have

$PQ=PR$

$\Rightarrow \angle R=\angle Q$ (Angles opposite to equal sides are also equal)

Also $\angle Q=2\times \angle P$

Sum of all angles of a triangle $={180}^{\circ }$

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

Substituting from above results

$\Rightarrow \angle Q+\angle Q+\frac{1}{2}\times \angle Q={180}^{\circ }$

$\Rightarrow \frac{5}{2}\times \angle Q={180}^{\circ }$

$\Rightarrow \angle Q={72}^{\circ }$