The diagonal of a rectangle ABCD intersect at O If BOC = 76 , find ODA - Maths - Understanding Quadrilaterals

Question

​The diagonal of a rectangle ABCD intersect at O If BOC = 76
, find ODA​

Brijendra Pal · Accepted Answer

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Given in rectangle ABCD, ∠BOC = 76°
∠BOC = ∠AOD [Vertically opposite angles are equal]
∠AOD = 76°
Since diagonal of a rectangle are equal and they bisect each
other
We can write OA = OB = OC = OD
Hence DAO is an isosceles triangle
⇒∠OAD = ∠ODA [Angles opposite to equal sides of a
triangle are equal]
Let ∠OAD = ∠ODA = x
∠OAD + ∠ODA +∠AOD = 180°
⇒ x + x + 76° = 180°
⇒ 2x = 104°
⇒ x = 52°
Hence ∠ODA = 52°

​The diagonal of a rectangle ABCD intersect at O. If BOC = 76 , find ODA​

The diagonal of a rectangle ABCD intersect at O. If BOC = 76 , find ODA