Question
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°
- 90°
- 94°
- 137°
✓
Answer
- 86°
$\angle\text{AOC}+\angle\text{COB}+\angle\text{BOD}+\angle\text{AOD}=360^\circ\dots(1)$
Now,
$\angle\text{AOC}+\angle\text{COB}+\angle\text{BOD}=274^\circ\dots(2)$ [Given]
From (1) and (2).
$274^\circ+\angle\text{AOD}=360^\circ$
$\Rightarrow\ \angle\text{AOD}=360^\circ-274^\circ$
$\Rightarrow\ \angle\text{AOD}=86^\circ$
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