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

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 = ?
(a) 40°
(b) 35°
(c) 45°
(d) 50°

 

Solution:

(a) 40°

Explanation:
OAD = ​∠OCB = 30o              (Alternate interior angles)
AOB + ∠BOC = 180o              (Linear pair of angles)
∴ ∠BOC = 180o − 70o = 110o       (∠ AOB = 70o)
In ∆BOC, we have:
OBC = 180o − (110o + 30o) = 40o
∴ ​∠DBC = 40o

 

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Pooja
April 3, 2023, 6:35 a.m.
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