The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O such that ∠DAC = 30° and ∠AOB = 70°. Then, ∠DBC = ?

Question

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O such that ∠ DAC = 30° and ∠ AOB = 70°. Then, ∠ DBC = ?

Philoid · Accepted Answer

In the given figure,

∠OAD = ∠OCB (Alternate interior angle)

∠OCB = 30°

∠AOB + ∠BOC = 180° (Linear pair)

70° + ∠BOC = 180°

∠BOC = 110°

Now, In ∆BOC,

∠OBC + ∠BOC + ∠OCB = 180°

∠OBC + 110° + 30° = 180°

∠OBC = 40°

∴ ∠DBC = 40°

Hence, Option A is correct.