Question

In $∆PQR$, if $PQ=QR$ and $\angle Q=100°$, then $\angle R$ is equal to?

• A. $40°$
• B. $80°$
• C. $120°$
• D. $50°$

Answer 1

The correct option is A

$40°$

Explanation of the correct option:

In $∆PQR$

$PQ=QR$[$\therefore$It is a isosceles triangle]

$\angle P=\angle R=x$

It is given that $\angle Q=100°$, then sum of interior angles of triangle is

$x+x+100°=180°$[$\because$Sum of interior angle of a triangle is $180°$]

$$\begin{gathered} \Rightarrow 2x=180°-100° \\ \Rightarrow 2x=80° \\ \Rightarrow x=40° \end{gathered}$$

Therefore, $\angle P=\angle R={40}^{\circ }$

Hence, the correct option is $\mathrm{Option}\left(\mathrm{A}\right)$.