MCQ
In the given figure, if $\angle\text{AOD}=135^\circ$ then $\angle\text{BOC}$ is equal to :
- A$25^\circ$
- ✓$45^\circ$
- C$52.5^\circ$
- D$62.5^\circ$
✓
Answer
Correct option: B.
$45^\circ$
We know that sum of the angles subtended by opposite sides of a quadrilateral having a circumscribed circle is $180^\circ .$
$\Rightarrow\angle\text{AOD}+\angle\text{BOC}=180^\circ$
$\Rightarrow135^\circ+\angle\text{BOC}=180^\circ$
$\Rightarrow\angle\text{BOC}=45^\circ$
$\Rightarrow\angle\text{AOD}+\angle\text{BOC}=180^\circ$
$\Rightarrow135^\circ+\angle\text{BOC}=180^\circ$
$\Rightarrow\angle\text{BOC}=45^\circ$
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