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$AB, CD EF$ are three concurrent lines passing through the point $O$ such that $OF$ bisects $∠ BOD$ . If $∠ BOF = 3 5^{\circ},$ find $∠ BOC ∠ AOD$ .

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∠ BOC = 11 0^{\circ}

∠ AOD = 11 0^{\circ}

∠ AOD = 7 0^{\circ}

None of these

answer is A.

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Detailed Solution

Given,

∠ BOF = 3 5^{\circ},

For

∠ BOD

, line

OF

is angle bisector. Thus, it divides

∠ BOD

into two same parts.

∴ ∠ BOF = 3 5^{\circ} = ∠ FOD

For straight line,

∠ BOF + ∠ FOD + ∠ AOD = 18 0^{\circ}

Put the values,

3 5^{\circ} + 3 5^{\circ} + ∠ AOD = 18 0^{\circ}

\Rightarrow ∠ AOD = 18 0^{\circ} - 7 0^{\circ}

\Rightarrow ∠ AOD = 11 0^{\circ}

Also, vertically opposite angles are equal in measure when 2 lines intersect.
Question Image

Thus,

\Rightarrow ∠ AOD = ∠ BOC = 11 0^{\circ}

So, option 1 and 2 are correct.

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