Question

In the given figure $O$ is the centre of the circle and $\angle AOC={120}^{\circ }$. What is the value of $\angle APC+\angle ABC$?

• A. ${120}^{\circ }$
• B. ${140}^{\circ }$
• C. ${160}^{\circ }$
• D. ${180}^{\circ }$

Answer 1

The correct option is D ${180}^{\circ }$

As $APCB$ is a cyclic quadrilateral, sum of its opposite angles are always equal to ${180}^o$.

Here, $\angle APC$ and $\angle ABC$ are the opposite angles of the cyclic quadrilateral.

Then clearly,

$\angle APC+\angle ABC={180}^o$.

Therefore, option $D$ is correct.