ABCD is a rectangle with ∠BAC = 32°. Determine ∠DBC.

Angle Suppose the diagonals AC and BD intersect at O.

Then, in ∆ OAB, we have

OA = OB [ diagonals of rectangle are equal and they bisect each other]

∠OAB =∠OBA

∠BAC=∠DBA

∠DBA = 32° [∠BAC = 32°(given)]

Now,

∠ABC = 90°

∠DBA +∠DBC = 90°

32° +∠DBC = 90°

∠DBC = 90° - 32° = 58°