The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠DAC = 32° and ∠AOB = 70°, then ∠DBC is equal to

Question

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠ DAC = 32° and ∠ AOB = 70°, then ∠ DBC is equal to

Philoid · Accepted Answer

Given: ∠AOB = 70°

∠DAC = 32°

∵ AD ∥ BC and AC is transversal

∴ ∠ACB = 32°

Now,

∠AOB + ∠BOC = 180°

⇒ 70° + ∠BOC = 180°

⇒ ∠BOC = 180° - 70°

⇒ ∠BOC = 110°

Sum of all angles of a triangle = 180°

⇒ ∠BOC + ∠BCO + ∠OBC = 180°

⇒ 110° + 32°+ ∠OBC = 180°

⇒ 142°+ ∠OBC = 180°

⇒ ∠OBC = 180° - 142°

⇒ ∠OBC = 38°

Hence, ∠DBC = 38°