Question

In the adjoining figure, O is the centre of the circle whose diameter is MN. Measures of some central angles are given. Find the measure of angle AOB.

• A. ${80}^{\circ }$
• B. ${70}^{\circ }$
• C. ${85}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is A ${80}^{\circ }$

Given, MN is the diameter of the circle.
Hence, $\angle MOA+\angle AOB+\angle BON={180}^{\circ }$
$\Rightarrow {80}^{\circ }+\angle AOB+{20}^{\circ }={180}^{\circ }$
$\Rightarrow \angle AOB={80}^{\circ }$