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