Question
AB, CD and EF are three concurrent lines passing throught the point O such that OF bisects $\angle\text{BOD}.$ If $\angle\text{BOF}=35^\circ,$ find $\angle\text{BOC}$ and $\angle\text{AOD}.$
✓
Answer
$\angle\text{BOF}=35^\circ$
$\therefore\angle\text{BOD}=2\angle\text{BOF}=70^\circ$ $[\because$ OF bisects $\angle\text{BOD}]$
$\angle\text{BOD}=\angle\text{AOC}=70^\circ$ [vertically opposite angles]
Now,
$\angle\text{BOC}+\angle\text{AOC}=180^\circ$ [linear pair]
$\Rightarrow\ \angle\text{BOC}+70^\circ=180^\circ$
$\Rightarrow\ \angle\text{BOC}=110^\circ$
$\therefore\ \angle\text{AOD}=\angle\text{BOC}=110^\circ$ [vertically opposite angles]
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