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

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

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14 Oct 2019, 00:31
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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 ]

$$A. 40^o$$

$$B. 45^o$$

$$C. 50^o$$

$$D. 55^o$$

$$E. 60^o$$

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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Senior Manager Joined: 01 Mar 2019 Posts: 267 Location: India Concentration: Strategy, Social Entrepreneurship Schools: Ross '22, ISB '20, NUS '20 GPA: 4 Re: The figure shows that line m is parallel to the line n, and l is paral [#permalink] Show Tags 14 Oct 2019, 01:30 Angle at BAD =80° 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 Posted from my mobile device Manager 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] Show Tags 14 Oct 2019, 20:40 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 Joined: 28 Feb 2014 Posts: 179 Location: India Concentration: General Management, International Business GPA: 3.97 WE: Engineering (Education) Re: The figure shows that line m is parallel to the line n, and l is paral [#permalink] Show Tags 14 Oct 2019, 21:17 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 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] Show Tags 16 Oct 2019, 02:53 => 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 $$<BDC=55°.$$ Therefore, D is the answer. Answer: D _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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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