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The figure shows that line m is parallel to the line n, and

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by Max@Math Revolution » Sun Oct 13, 2019 11:13 pm
[GMAT math practice question]

The figure shows that line m is parallel to the line n, and l is parallel to k. Moreover, ∠ CBD=45, ∠ FAE=80. What is ∠ BDC?

Image

A. 40
B. 45
C. 50
D. 55
E. 60
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by Aditi Goyal » Mon Oct 14, 2019 12:44 am
Angle EAF is vertically opposite to angle BAD. Angle EAF=80
Therefore Angle BAD = 80
SInce m||n and l || k, it is a forms a parallelogram
Angle BAD = Angle BCD (opposite angles) = 80
In triangle BCD, angle BDC = 180 -(80+45) = 55
therefore angle BCD = 80 $$\angle$$ $$\angle$$
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by Aditi Goyal » Mon Oct 14, 2019 12:47 am
Aditi Goyal wrote:Angle EAF is vertically opposite to angle BAD. Angle EAF=80
Therefore Angle BAD = 80
SInce m||n and l || k, it forms a parallelogram
Angle BAD = Angle BCD (opposite angles) = 80
In triangle BCD, angle BDC = 180 -(80+45) = 55
therefore angle BCD = 80 $$\angle$$ $$\angle$$
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by Max@Math Revolution » Wed Oct 16, 2019 1:14 am
=>

Image

Since lines m and n are parallel, we have < FBG=< FAE=80° and 80°+< ABD+45°=180°.
Then we have 125°+< ABD=180 and < ABD=55°.
Since < ABD and < BDC are alternate interior angles, they are congruent and < BDC=55°.

Therefore, D is the answer.
Answer: D
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