Question

Given that arc, $\text{AB}$ subtends an angle of ${40}^{\circ }$ to the center of a circle. The angle made by arc $\text{AB}$ in the remaining part of the circle is

• A. ${20}^{\circ }$
• B. ${80}^{\circ }$
• C. ${60}^{\circ }$
• D. ${100}^{\circ }$

Answer 1

The correct option is A ${20}^{\circ }$



Given that,
Angle made by arc $\text{AB}$ $={40}^{\circ }$
Note: Angle subtended by an arc at the centre is double of the angle subtended by the arc at any point remaining part of the circle.

So, the angle made by the arc $\text{AB}$ in the remaingning part of the cirlce at $C$ will be half of the angle 40${}^{\circ }$ subtended by the arc $\text{AB}$ at the centre
i.e. $\frac{{40}^{\circ }}{2}={20}^{\circ }$