Question

In the given figure, O is the centre of the circle and $\angle ABC={36}^{\circ }$. The measure of $\angle AOC$ is :

• A. ${36}^{\circ }$
• B. ${72}^{\circ }$
• C. ${144}^{\circ }$
• D. ${18}^{\circ }$

Answer 1

The correct option is B ${72}^{\circ }$

From the figure, if we draw a straight line from A to C, we get line AC which is a chord of the circle .

Angle subtended by any chord at the centre of a circle is

double than that of the angle subtended by that chord at any point on circumference of the circle.

$\therefore \angle AOC$ = $2.\angle ABC$

So $\angle AOC$ = ${72}^{\circ }$

therefore option B will be the answer.