In the given figure, O is the centre of a circle and \[\angle OAB=50{}^\circ .\]Then, \[\angle BOD\] is equal to |
A) \[130{}^\circ \]
B) \[50{}^\circ \]
C) \[100{}^\circ \]
D) \[80{}^\circ \]
Correct Answer: C
Solution :
\[OA=OB\]\[\Rightarrow \]\[\angle OBA=\angle OAB=50{}^\circ \] |
[angle substend by same segments, i.e. radius] |
In \[\Delta OAB,\]\[\angle OAB+\angle OBA+\angle AOB=180{}^\circ \] |
\[\Rightarrow \]\[50{}^\circ +50{}^\circ +\angle AOB=180{}^\circ \] |
\[\Rightarrow \] \[\angle AOB=80{}^\circ \] |
\[\therefore \]\[\angle BOD=(180{}^\circ =80{}^\circ )=100{}^\circ \] |
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