Question

In the figure, $O$ is the centre of the circle. Find $\angle ABC$.

• A. ${160}^o$
• B. ${100}^o$
• C. ${90}^o$
• D. ${80}^o$

Answer 1

The correct option is D ${80}^o$


As reflex $\angle AOC={200}^o$
so,
$obtuse\angle AOC+reflex\angle AOC={360}^o$
$obtuse\angle AOC+{200}^o={360}^o$
$obtuse\angle AOC={160}^o$

Now,
$\angle ABC=\frac{obtuse\angle AOC}{2}\text{(angle subtended by minor arc AC at rest part of circumference is half of the angle made at centre)}$
$\angle ABC=\frac{{160}^o}{2}$
$\angle ABC={80}^o$

So, option $\left(d\right)$ correct.