Question

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

• A. 60${}^{\circ }$
• B. 40${}^{\circ }$
• C. 75${}^{\circ }$
• D. 80${}^{\circ }$

Answer 1

The correct option is A 60${}^{\circ }$

Recall that the angle subtended by an arc at the centre of the circle is twice the angle subtended by this arc in the other segment.

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 in the other segment. So it should be half the angle subtended by the arc at the centre (which is ${120}^{\circ })$. Half of ${120}^{\circ }$ is ${60}^{\circ }$. So $\angle APB={60}^{\circ }$.