Question

In the given figure, O is the centre of the circle. The value of x(in degrees) is

• A. ${75}^{\circ }$
• B. ${55}^{\circ }$
• C. ${125}^{\circ }$
• D. ${110}^{\circ }$

Answer 1

The correct option is C ${125}^{\circ }$

Reflex $\angle O={360}^{\circ }-{110}^{\circ }={250}^{\circ }$
$\therefore ABC=\frac{1}{2}\times {250}^{\circ }={125}^{\circ }$
(Angle subtended by an arc at the centre is twice the angle at any remaining part of the $⨀$ce of the circle)
$\therefore x=\angle ABC=\frac{1}{2}={125}^{\circ }$ (Vertically opposite angles )