Question

In the figure, O is the centre of the circle such that $\angle AOC={130}^o,then\angle ABC=$

• A. ${130}^o$
• B. ${115}^o$
• C. ${65}^o$
• D. ${165}^o$

Answer 1

The correct option is B

${115}^o$

O is the centre of the circle and $AOC={130}^o$

Reflex $\angle AOC={360}^o-{130}^o={230}^o$

Now, arc ADB subtends $\angle AOC$ at the centre and $\angle ABC$ at the remaining part of the circle.

$\therefore \angle ABC=\frac{1}{2}reflex\angle AOC$

$=\frac{1}{2}\times {230}^o={115}^o$