Question

In the figure above (not to scale) O is the centre of the circle $\angle OAB={60}^{\circ }$ and $\angle OCB={70}^{\circ }$ Then find the $\angle AOC$

• A. ${150}^{\circ }$
• B. ${120}^{\circ }$
• C. ${100}^{\circ }$
• D. ${80}^{\circ }$

Answer 1

The correct option is C ${100}^{\circ }$

Given that:

$\angle OAB={60}^{\circ },\angle OCB={70}^{\circ }$

To find:

$\angle AOC=?$

Solution:

$\angle ABC=\frac{1}{2}\times reflex\angle AOC$ (Angle at the centre is twice of angle subtended by the chord at the circumference.)

or, $\angle ABC=\frac{1}{2}\times ({360}^{\circ }-\angle AOC)$

or, $\angle ABC={180}^{\circ }-\frac{\angle AOC}{2}$

Now,

$\angle ABC+\angle OCB+\angle AOC+\angle OAB={360}^{\circ }$

or, ${180}^{\circ }-\frac{\angle AOC}{2}+{70}^{\circ }+\angle AOC+{60}^{\circ }={360}^{\circ }$

or, $\frac{\angle AOC}{2}={360}^{\circ }-{180}^{\circ }-{130}^{\circ }$

or, $\frac{\angle AOC}{2}={50}^{\circ }$

or, $\angle AOC={100}^{\circ }$

Hence, C is the correct option.