Mathematics
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
24°
86°
38°
32°
Answer
From figure,
∠ACB = ∠DAC = 32° (Alternate angles are equal)
AC is a straight line.
⇒ ∠AOB + ∠BOC = 180°
⇒ 70° + ∠BOC = 180°
⇒ ∠BOC = 180° - 70°
⇒ ∠BOC = 110°.
In △OBC,
⇒ ∠BOC + ∠OBC + ∠OCB = 180°
From figure,
⇒ ∠OCB = ∠ACB = 32°
⇒ 110° + ∠OBC + 32° = 180°
⇒ ∠OBC = 180° - 142° = 38°.
From figure,
∠DBC = ∠OBC = 38°.
Hence, Option 3 is the correct option.
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