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Question
In a parallelogram ABCD, if ∠DAB = 75° and ∠DBC = 60°, then ∠BDC =
Options
75°
60°
45°
55°
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Solution
Parallelogram can be drawn as :
We know that the opposite angles of a parallelogram are equal.
Therefore, ∠DCB = ∠DAC
∠DBC = 75°
By angle sum property of a triangle:
∠DBC + ∠DCB + ∠BDC = 180°
60° + 75 + ∠BCD = 180°
135° + ∠BDC = 180°
∠BDC = 180°-135°
∠BDC = 45°
Thus, ∠BDC measures 45°.
Hence the correct choice is (c).
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