$AB, CD$ 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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Updated on: 10-Oct-2022

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