Question

the diagonals of a rectangle ABCD intersect in O if angle BOC is equal to 70 degree find angle oda and angle abo​

Answer 1

Answer:

∠BOC = ∠AOD[Vertically opposite angles are equal]

∠AOD = 70° Since diagonal of a rectangle are equal and they bisect each other.

We can write OA = OB = OC = OD

Hence DAOD 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 + 70° = 180°

⇒2x = 110°

⇒x = 55° Hence ∠ODA = 55°

Answer 2

∠BOC = ∠AOD[Vertically opposite angles are equal]

∠AOD = 70° Since diagonal of a rectangle are equal and they bisect each other.

We can write OA = OB = OC = OD

Hence DAOD 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 + 70° = 180°

⇒2x = 110°

⇒x = 55° Hence ∠ODA = 55°

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