Question

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

विकल्प

• 24º

• 86º

• 38º

• 32º

Answer 1

The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠DAC = 32º and ∠AOB = 70º, then ∠DBC is equal to 38º.

Explanation:

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°