Question

In a$∆PQR$, if $QO$and $RO$ are internal angle bisectors of$\angle Q$ and$\angle R$respectively and$\angle QPR=70°$, then $\angle QOR$ is

• A. $110°$
• B. $125°$
• C. $45°$
• D. $130°$

Answer 1

The correct option is B

$125°$

The explanation for the correct option:

Find the angle $\angle QOR$:

Given, $\angle QPR=70°$

Let the $\angle OQR$ and $\angle ORQ$ be $x$ and $y$

Here, $QO$and $RO$ are angle bisectors of $\angle PQR$ and $\angle PRQ$ respectively.

So, $\angle PQR=2x$

$\angle PRQ=2y$

In $∆PQR$, by angle sum property of a triangle

$$\begin{gathered} \angle QPR+\angle PRQ+\angle RQP=180° \\ \Rightarrow 70°+2x+2y=180° \\ \Rightarrow x+y=\frac{110°}{2} \\ \Rightarrow x+y=55° \end{gathered}$$

In $△OQR$, by angle sum property of a triangle.

$\angle OQR+\angle QRO+\angle QOR=180°$

$$\begin{gathered} \Rightarrow x+y+\angle QOR=180° \\ \Rightarrow \angle QOR=125° \end{gathered}$$

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