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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8141
GMAT 1: 760 Q51 V42 GPA: 3.82
The figure shows that line m is parallel to the line n, and l is paral  [#permalink]

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Difficulty:   15% (low)

Question Stats: 79% (01:12) correct 21% (01:27) wrong based on 28 sessions

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[GMAT math practice question]

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

Attachment: 10.14ps.png [ 19.74 KiB | Viewed 353 times ]

$$A. 40^o$$

$$B. 45^o$$

$$C. 50^o$$

$$D. 55^o$$

$$E. 60^o$$

_________________
Senior Manager  G
Joined: 01 Mar 2019
Posts: 267
Location: India
Concentration: Strategy, Social Entrepreneurship
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Re: The figure shows that line m is parallel to the line n, and l is paral  [#permalink]

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Since ABCD is a parallelogram
Opp angles are equal and sum of angles is 360°

So angle ADC will be 100°

Angle CBD = Angle ADB =45°

So angle BDC will be 100-45= 55°

OA:D

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Manager  G
Joined: 22 Feb 2018
Posts: 220
Location: India
Concentration: Entrepreneurship, Healthcare
Re: The figure shows that line m is parallel to the line n, and l is paral  [#permalink]

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As m and n & k and l are parallel, ABCD is a parallelogram.
As ABCD is //, it's two opposite angles are same.
<EAF =80°, then<DAB is also 80°, as both are vertically opposite of the two straight lines.
It implies that <DCB =80°.
Triangle DCB, CBD+BCD+BDC= 180
80+45+BDC=180
BDC =55.
Hence, D.
Manager  G
Joined: 28 Feb 2014
Posts: 179
Location: India
GPA: 3.97
WE: Engineering (Education)
Re: The figure shows that line m is parallel to the line n, and l is paral  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

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

Attachment:
10.14ps.png

$$A. 40^o$$

$$B. 45^o$$

$$C. 50^o$$

$$D. 55^o$$

$$E. 60^o$$

Angle DAB=80 (vertically opposite angle)

Angle DAB + ABC = 180 ( Sum is supplementary)
Angle ABC = 100
Angle ABC = Angle ABD + DBC
Therefore, Angle ABD = 100- 45 = 55

Angle ABD = Angle BDC = 55 ( Alternate interior angles)

D is correct
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8141
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The figure shows that line m is parallel to the line n, and l is paral  [#permalink]

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=>

Attachment: 10.14ds(a).png [ 19.12 KiB | Viewed 145 times ]

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 $$<BDC=55°.$$

_________________ Re: The figure shows that line m is parallel to the line n, and l is paral   [#permalink] 16 Oct 2019, 02:53
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