MCQ
Two straight lines $AB$ and $CD$ intersect one another at the point $O$. If $\angle\text{AOC}+\angle\text{COB}+\angle\text{BOD}=274^\circ, $ then $\angle\text{AOD}=$
- ✓$86^{\circ}$
- B$137^{\circ}$
- C$90^{\circ}$
- D$94^{\circ}$
✓
Answer
Correct option: A.
$86^{\circ}$
Given,
$\angle\text{AOC}+\angle\text{COB}+\angle\text{BOD}=274^\circ\text{ (i)}$
$\angle\text{AOD}+\angle\text{AOC}+\angle\text{COB}+\angle\text{BOD}=360^\circ$(Angles at a point)
$\angle\text{AOD}+274^\circ=360^\circ$
$\angle\text{AOD}=86^\circ.$
$\angle\text{AOC}+\angle\text{COB}+\angle\text{BOD}=274^\circ\text{ (i)}$
$\angle\text{AOD}+\angle\text{AOC}+\angle\text{COB}+\angle\text{BOD}=360^\circ$(Angles at a point)
$\angle\text{AOD}+274^\circ=360^\circ$
$\angle\text{AOD}=86^\circ.$
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