Question

In a $△PQR$ the angle bisectors of $\angle PQR$ and $\angle PRQ$ meet t O. If $\angle QPR={80}^o$, what is the measure of $\angle QOR$?

• A. ${80}^o$
• B. ${130}^o$
• C. ${160}^o$
• D. ${90}^o$

Answer 1

The correct option is B ${130}^o$

$\angle QPR=80°$

$\angle PQR+\angle QPR+\angle QRP=180°$

$\angle PQR+\angle QRP=100°$

$2(x+y)=100°$

$x+y=50°$

So, in $△QOR$

$x+y+\angle QOR=180°$

$\therefore \angle QOR=180°-50°$

$=130°$