Question

In the given figure∠BOD = 54° Find the measure of the angles ∠BOC , ∠COA and ∠AOD.​

Answer 1

Given:-

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• ∠BOD = 54°

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To Find:-

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• the measure of the angles ∠BOC , ∠COA and ∠AOD.

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STEP BY STEP EXPLANATION:-

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As ∠BOD and ∠BOC from a straight Line:

∠BOD + ∠BOC = 180°

54° + ∠BOC = 180°

∠BOC = 180° - 54°

∠BOC = 126°

As ∠BOD and ∠COA are vertically opposite angle:

∠COA = ∠BOD $\longrightarrow$∠COA = 54°

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As ∠AOD and ∠BOC are vertically opposite angle:

∠AOD = ∠BOC $\longrightarrow$∠AOD = 126°

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∴ Hence, ∠BOC = 126° , ∠COA = 54° and ∠AOD = 126°

Answer 2

Solution :-

* C - O - D is a straight line..

* OB is a line transversal to line COD .

→ ∠BOD = 54° (Given)

→ ∠BOC = 180° - ∠BOD { As COD is a straight line, So , complete angle is Equal to 180°} .

→ ∠BOC = 180° - 54°

→ ∠BOC = 126° (Ans.)

Now,

→ ∠BOD = 54° (Given)

→ ∠BOD = ∠COA { vertically opposite angles states that angles opposite each other when two lines cross are always equal.}

So ,

→ ∠COA = 54° (Ans.)

Similarly,

→ ∠AOD = 126° (Ans.) { Equal to vertically opposite angles of ∠BOC or, A-O-B is also a straight line So, complete angle.}