Question

Question 115

In $\Delta PQR$ of the given figure, PQ = PR. Find the measures of $\angle Q$ and $\angle R$

Answer 1

Since, PQ = PR [given]
$\therefore \angle Q=\angle R$ [ Since Angle opposite to the equal sides are equal. ]
Let ,
$\angle$Q=$\angle$R = x (say )
As we know, $\angle P+\angle Q+\angle R={180}^{\circ }$ [angle sum property of a triangle]
$\Rightarrow {30}^{\circ }+x+x={180}^{\circ }\Rightarrow 2x={150}^{\circ }\Rightarrow x={75}^{\circ }$
Hence, $\angle Q=\angle R={75}^{\circ }$