Question

If $\angle BOC=80°$and OA bisects $\angle BAC$, then find the value of $\angle ABO$ in degrees.

• A. 20

Answer 1

The correct option is A 20
Given: $\angle BOC=80°$
OA is a line which bisect the $\angle BAC$


We know that, an angle subtented by an arc at the centre is double the angle subtented by it at any point on the remaining part of the circle.
$\Rightarrow \angle BOC=2\times \angle BAC$
$\therefore \angle BAC=40°$
OA is a line which bisect the $\angle BAC$
Thus, $\angle BAO=20°$
Consider $\Delta AOB,$
$OA=OB=r$
$\angle OAB=\angle OBA$ ..... (angles opposite equal sides are equal)
Hence, $\angle ABO=20°$