question_answer

In the diagram, 0 is the centre of the circle. The angles CBD is equal to

A) \[25{}^\circ \]  

B)  \[50{}^\circ \]

C) \[40{}^\circ \]

D) \[130{}^\circ \]

Correct Answer: A

Solution :

 Angle subtended by Arc ABC at the centre     \[\therefore \]Angle subtended by Arc ABC at any point on  the circumference \[={{25}^{o}}\]             \[\therefore \]  \[\angle ABC={{180}^{o}}-{{25}^{o}}={{155}^{o}}\]        [Since opposite angles of a cyclic quadrilateral  are supplementary]                      \[\therefore \]  \[\angle CBD={{180}^{o}}-{{155}^{o}}={{25}^{o}}\]