In the figure shown, ABCD is a parallelogram, DAO = BAO and ADO = CDO. Find the measure of AOD.
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Answered by
16
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°.
Answered by
5
Answer:
Your answer is angle AOD = 90 degree
Hope it will help
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