Question

In the given figure $\text{O}$ is the center of the circle and measure of $\angle \text{AOC}$ is ${100}^{\circ }$ what is the value of $\angle \text{ADC}$ ?

• A. ${30}^{\circ }$
• B. ${40}^{\circ }$
• C. ${50}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is C ${50}^{\circ }$

The angle subtended by an arc at the center of the circle is twice the angle subtended by it on the circumference of the circle.

$⟹\angle \text{ADC}=\frac{1}{2}\angle \text{AOC}$

$=\frac{1}{2}\times 100$

$={50}^{\circ }$