In figure (3) given below, ABCD is a kite and diagonals intersect at O. If ∠DAB = 112° and ∠DCB = 64°, find ∠ODC and ∠OBA.

Diagonals of a kite bisect the vertex angles. ∴ ∠OCD = = 32° and ∠OAB = = 56° Diagonals of a kite are perpendicular to each other. ∴ ∠DOC = 90° ⇒ ∠OCD + ∠DOC + ∠ODC = 180° ⇒ 32° + 90° + ∠ODC = 180° ⇒ ∠ODC = 58°. Diagonals of a kite are perpendicular to each other. ∴ ∠AOB = 90° ⇒ ∠AOB + ∠OAB + ∠OBA = 180° ⇒ 90° + 56° + ∠OBA = 180° ⇒ ∠OBA = 180° - 146° = 34°. Hence, ∠OBA = 34° and ∠ODC = 58°.