Question

From the figure shown, find $\angle$ APB in degrees, if $\angle$ AOB = ${120}^{\circ }$.

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Answer 1

The angle subtended by an arc at the centre of the circle is twice the angle subtended by this arc at any point on the remaining part of the circle.

Now the angle subtended by the arc at the centre is $\angle$ AOB, which is ${120}^{\circ }$. $\angle$APB is the angle subtended by the arc at a point on the remaining part of the circle. So it should be half the angle subtended at the centre (which is ${120}^{\circ }$). Half of ${120}^{\circ }$ is ${60}^{\circ }$, so angle $\angle$ APB = ${60}^{\circ }$.