Question

The diagonals of a rectangle ABCD meet at O, If ∠BOC = 44°, find ∠OAD.

Answer 1

The rectangle ABCD is given as:

We have,

 ∠BOC +∠BOA = 180° (Linear pair)

44° +∠BOA = 180°

         ∠BOA = 180° -44°

         ∠BOA = 136°

Since, diagonals of a rectangle are equal and they bisect each other. Therefore, in ΔOAB, we have

OA = OB (Angles opposite to equal sides are equal.)

Therefore,

∠1 = ∠2

Now,in ΔOAB, we have

∠BOA + ∠1 +∠2 = 180

       ∠BOA + 2∠1 = 180°

                      2∠1 = 44°

                        ∠1 = 22°

Since, each angle of a rectangle is a right angle.

Therefore,

    ∠BAD = 90°

  ∠1+∠3 = 90°

22° +∠3 = 90°

         ∠3 = 68°

Thus, ∠OAD = 68°

Hence, the measure of∠OAD is 68°.