MCQ
In figure, if $\angle \text{A O B} =125^{\circ}$, then $\angle \text{C O D}$ is equal to
- A$62.5^{\circ}$
- B$45^{\circ}$
- C$35^{\circ}$
- ✓$55^{\circ}$
✓
Answer
Correct option: D.
$55^{\circ}$
We know that the opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.
$\Rightarrow \angle A O B+\angle C O D=180^{\circ}$
$\Rightarrow \angle C O D=180^{\circ}-\angle A O B=180^{\circ}-125^{\circ}=55^{\circ}$
$\Rightarrow \angle A O B+\angle C O D=180^{\circ}$
$\Rightarrow \angle C O D=180^{\circ}-\angle A O B=180^{\circ}-125^{\circ}=55^{\circ}$
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