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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 ______.
Options
24º
86º
38º
32º
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Solution
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°
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