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$AB, CD$ and $EF$ are three concurrent lines passing through the point $O$ such that $OF$ bisects $\angle BOD$. If $\angle BOF = 35^o$, find $\angle BOC$ and $\angle AOD$.
Given:
$AB, CD$ and $EF$ are three concurrent lines passing through the point $O$ such that $OF$ bisects $\angle BOD$.
$\angle BOF = 35^o$
To do:
We have to find $\angle BOC$ and $\angle AOD$.
Solution:
$OF$ bisects $\angle BOD$.
Therefore,
$\angle DOF = \angle BOF = 35^o$
$\angle BOD = 35^o + 35^o = 70^o$
$\angle BOC + \angle BOD = 180^o$ (Linear pair)
$\angle BOC + 70^o = 180^o$
$\angle BOC = 180^o - 70^o = 110^o$
$\angle AOD = \angle BOC = 110^o$ (Vertically opposite angles)
Hence, $\angle BOC = 110^o$ and $\angle AOD =110^o$.
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