Question

If O is the center of the circle, then find the value of $\theta$ in the adjoining figure.
[2 Marks]

Answer 1

Angle made in full circle $={360}^{\circ }$
So, ${120}^{\circ }+{90}^{\circ }$ + Angle at centre = ${360}^{\circ }$

$\Rightarrow$ Angle at centre $={360}^{\circ }-{210}^{\circ }={150}^{\circ }$ [1 Mark]

$\therefore$ $\theta$ $=\frac{1}{2}(\text{Angle at the centre)}=\frac{{150}^{\circ }}{2}={75}^{\circ }$
[Since angle subtended by the arc at the circumference is half the angle subtended at the centre]
[1 Mark]