Question

In the figure shown, ABCD is a parallelogram, DAO = BAO and ADO = CDO. Find the measure of AOD.​

Answer 1

Solution :-

Given that,

∠ DAO = ∠ BAO -----(1)

∠ ADO = ∠ CDO ------(2)

As we know that,

∠ DAO + ∠ BAO + ∠ ADO + ∠ CDO = 180° [Co interior angle ]

By using (1) and (2),

∠ DAO + ∠ DAO + ∠ ADO + ∠ ADO = 180°

2 ∠ DAO + 2 ∠ ADO = 180°

2 ( ∠ DAO + ∠ ADO ) = 180°

∠ DAO + ∠ ADO = 180°/2

∠ DAO + ∠ ADO = 90° ----(3)

As we know that, by applying angle sum property in ∆ AOD, we get :

∠ DAO + ∠ ADO + ∠ AOD = 180°

By using (3) we get,

90° + ∠ AOD = 180°

∠ AOD = 180° - 90°

∠ AOD = 90°

So the value of ∠ AOD is 90°.

Answer 2

Answer:

Your answer is angle AOD = 90 degree

Hope it will help

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