Question

the diagonal of a rectangle ABCD intersect at O if BOC is equal to 70 degree find angle OdA

Answer 1

Answer:

55°

Step-by-step explanation:

Refer to the attached figure.

Given : ABCD is a rectangle, ∠BOC = 70°

To find: ∠ODA

Solution:

We know that Diagonals of rectangle are equal and bisect each other

         ∴ AC = BD

      (1/2)AC = (1/2)BD

            CO = BO ---- ( i )

In ΔBOC

           CO = BO     [ From ( i ) ]

   ∴∠OCB = ∠OBC  [Angles opposite to equal sides are also equal]

Now,

 ∠OCB + ∠OBC + ∠BOC = 180° [ Angle Sum Property of Triangle]

      ∠OBC + ∠OBC + 70° = 180°      [∵∠OCB = ∠OBC and ∠BOC = 70°]

                       2∠OBC = 110°

                         ∠OBC = 55°

Also, ∠ODA = ∠OBC                       [ Alternate Interior Angles]

   ∴ ∠ODA  = 55°

Answer 2

Answer:

angle ODA=55°

HOPE IT HELPS