Question

In a triangle ABC, O is the centre of incircle PQR, $\angle BAC={65}^{\circ },\angle BCA={75}^{\circ }$, find $\angle ROQ$:

• A. ${80}^{\circ }$
• B. ${120}^{\circ }$
• C. ${140}^{\circ }$
• D. can't be determined

Answer 1

The correct option is C ${140}^{\circ }$

$\angle ABC={180}^{\circ }-({65}^{\circ }+{75}^{\circ })={40}^{\circ }\angle ORB=\angle OQB={90}^{\circ }\therefore \angle ROQ={360}^{\circ }-({90}^{\circ }+{90}^{\circ }+{40}^{\circ })\therefore \angle ROQ={140}^{\circ }$