question_answer

AB and CD are the diameters of a circle C (O, r). If\[\angle OBD=50{}^\circ \], then the measure of \[\angle AOC\] is

A)  \[80{}^\circ \] 

B)  \[40{}^\circ \]

C)  \[100{}^\circ \]

D)  \[25{}^\circ \]

Correct Answer: A

Solution :

\[\because \]       \[\angle OBD=50{}^\circ \] \[\because \]    \[\Delta OBD,OB=OD=r=\]radius \[\therefore \,\,\,\,\]          \[\,\angle BOD=180{}^\circ -(50{}^\circ +50{}^\circ )=80{}^\circ \] \[\therefore \,\,\,\,\]          \[\angle AOC=\angle BOD=80{}^\circ \]