MCQ
In the given figure, if $\angle\text{ABC} = 45^\circ,$ then $\angle\text{AOC} =$
- A$45^\circ$
- B$60^\circ$
- C$75^\circ$
- ✓$90^\circ$
✓
Answer
Correct option: D.
$90^\circ$
$\angle\text{AOC}$ is made by arc $\widehat{\text{AC}}$ at centre and $\angle\text{ABC}$ is made by $\widehat{\text{AC}}$ on circumference in major segment.
$\Rightarrow\angle\text{ABC}=\frac{1}{2}\angle\text{AOC}$
$\Rightarrow\angle\text{AOC}=2\times\angle\text{ABC}$
$=2\times45^\circ=90^\circ$
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