Question

The diagnol of a rectangle ABCD intersect at O. if <BOC=70°. Find <ODA

Answer 1

Hey there

Given in rectangle ABCD, ∠BOC = 70°

∠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°

Hope this helps

Answer 2

its 55° as shown due to the opposite sides equal