Question

In the given figure, O is the center of the incircle of $△$ABC. If $\angle BAC$ = ${65}^{\circ }$ and $\angle BCA$ = ${75}^{\circ }$, then find $\angle ROQ$.

• A. 80°
• B. 120°
• C. 140°
• D. Can't be determined

Answer 1

The correct option is C

140°

In triangle ABC

$\angle A+\angle B+\angle C={180}^{\circ }$

${65}^{\circ }+\angle B+{75}^{\circ }={180}^{\circ }$

$\angle B={40}^{\circ }$

We know that $\angle ORB={90}^{\circ }$ and $\angle OQB={90}^{\circ }$

$\angle ROQ={180}^{\circ }-\angle B$

$\angle ROQ={180}^{\circ }–{40}^{\circ }={140}^{\circ }$