Question

In the given figure, O is the centre of the circle and $\angle AOB={80}^{\circ }$, then match the following

• A. 40°
• B. 90°
• C. 180°

Answer 1

AOC is a straight line, so $\angle AOC$ should be a straight angle. Therefore $\angle AOC$= ${180}^{\circ }$.

Diameter is also a chord of the circle .The angle subtended by AC at the center is $\angle$AOC = ${180}^{\circ }$

Since angle subtended by a chord at the center is equal to twice the angle subtended by chord at any point on the circle,

We get $\angle AOC$ = 2 $\angle ABC$ = ${180}^{\circ }$

$\angle ABC$ = ${90}^{\circ }$

$\angle ACB$= $\frac{1}{2}$ $\angle AOB$ = $\frac{80}{2}$ = ${40}^{\circ }$