MCQ
In the given figure, $\angle\text{OEB} = 75^\circ,\angle\text{OBE}=55^\circ$ and $\angle\text{OCD}=100^\circ.$ Then $\angle\text{ODC}=?$
- ✓$30^\circ$
- B$25^\circ$
- C$35^\circ$
- D$20^\circ$
✓
Answer
Correct option: A.
$30^\circ$
In $\triangle\text{OEB}$
$\angle\text{OEB}+\angle\text{EBO}+\angle\text{BOE}=180^\circ$ (Angle sum property)
$75^\circ+55\circ+\angle\text{BOE}=180^\circ$
$\angle\text{BOE}=50^\circ$
$\angle\text{BOE}=\angle\text{COD}=50^\circ$ (vertically opposite angle)
In $\triangle\text{ODC}$
$\angle\text{ODC}+\angle\text{DOC}+\angle\text{DCO}=180^\circ$
$\angle\text{ODC}=180^\circ-100^\circ-50^\circ$
$\angle\text{ODC}=30^\circ$
$\angle\text{OEB}+\angle\text{EBO}+\angle\text{BOE}=180^\circ$ (Angle sum property)
$75^\circ+55\circ+\angle\text{BOE}=180^\circ$
$\angle\text{BOE}=50^\circ$
$\angle\text{BOE}=\angle\text{COD}=50^\circ$ (vertically opposite angle)
In $\triangle\text{ODC}$
$\angle\text{ODC}+\angle\text{DOC}+\angle\text{DCO}=180^\circ$
$\angle\text{ODC}=180^\circ-100^\circ-50^\circ$
$\angle\text{ODC}=30^\circ$
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