Question

If O is the center of the circle, then the value of $\theta$ in the adjoining figure is

• A. ${45}^{\circ }$
• B. ${60}^{\circ }$
• C. ${90}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

The correct option is D ${75}^{\circ }$

Angle made in full circle $={360}^{\circ }$
So, ${120}^{\circ }+{90}^{\circ }$ +Angle at centre =${360}^{\circ }$
$\Rightarrow$ Angle at centre $={360}^{\circ }-{210}^{\circ }={150}^{\circ }$
$\therefore$ Angle at circumference of a circle
$=\frac{1}{2}(\text{Angle at the centre)}=\frac{{150}^{\circ }}{2}={75}^{\circ }$