Question

If ABCD is a rectangle with ∠BAC = 32°, find the measure of ∠DBC.

Answer 1

Figure is given as :

Suppose the diagonals AC and BD intersect at O.

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,

∠OAB = ∠OBA

∠BAC = ∠DBA

But, ∠BAC = 32°

∠DBA = 32°

Now,

              ∠ABC = 90°

∠DBA + ∠DBC = 90°

      32° +∠DBC = 90°

               ∠DBC = 58°

Hence, the measure of ∠DBC is 58°.