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The figure below shows parallelogram ABCD

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The figure below shows parallelogram ABCD

by Max@Math Revolution » Mon Feb 10, 2020 12:50 am
[GMAT math practice question]

The figure below shows parallelogram ABCD where ∠DAC = 60 and ∠DBC = 30. What is ∠BDC?
2.10PS.png
A. 15
B. 30
C. 45
D. 60
E. 75
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Re: The figure below shows parallelogram ABCD

by Max@Math Revolution » Wed Feb 12, 2020 12:19 am
=>

We have ∠OCB = ∠OAD = 60 since they are alternate interior angles. Since ∠OBC = 30°, we have ∠BOC = 180° – (30° + 60°) = 90°.
Then the two diagonals are perpendicular to each other, and quadrilateral ABCD is a rhombus.
Thus, triangle BCD is an isosceles with BC = DC.
Then we have ∠BDC = ∠DBC = 30°.

Therefore, B is the answer.
Answer: B
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