Question

In $△PQR$, $PQ=PR$, $\angle Q={65}^{\circ }$ then find $\angle P$

Answer 1

By using the theorem,If two sides of a triangle are equal then the opposite angles to the sides are equal.

$\Rightarrow$ If $PQ=PR$ then $\angle Q=\angle R$

In $△PQR$,

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

$\Rightarrow \angle P+\angle Q+\angle R={180}^{\circ }$ since $\angle Q=\angle R={65}^{\circ }$(given)

$\Rightarrow \angle P+2\times {65}^{\circ }={180}^{\circ }$

$\Rightarrow \angle P={180}^{\circ }-{130}^{\circ }={50}^{\circ }$

$\therefore \angle P={50}^{\circ }$