Question

ABCE is a cyclic quadrilateral. 'O' is the centre of the circle and $\angle AOC={150}^{\circ }$, then the value of $\angle CBD$:

• A. ${225}^{\circ }$
• B. ${128}^{\circ }$
• C. ${150}^{\circ }$
• D. ${75}^{\circ }$

Answer 1

Answer: (D)

${75}^{\circ }$

Angle subtended at the center is twice the angle subtended anywhere on the arc. So

$\angle AEC=\frac{1}{2}\angle AOC={75}^o$

Opposite angles of cyclic quadrilateral $ABCE$ are supplementary. So

$\angle ABC=180-75={105}^o$

Clearly then $\angle CBD=180-\angle ABC={75}^o$

So option D is the right answer.