Question

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

• A. ${80}^o$
• B. ${120}^o$
• C. ${140}^o$
• D. Can't be determined

Answer 1

The correct option is C ${140}^o$

ABC is a triangle,
SO, $\angle A+\angle B+\angle C=180$
$65+\angle B+75=180$
$\angle B=40$
ROQB is a quadrilateral,
So, $\angle ORB+\angle B+\angle BQO+\angle ROQ=360$
$90+\angle B+90+40=360$
$\angle B=140$
Answer (C) $140$