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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8163
GMAT 1: 760 Q51 V42 GPA: 3.82
The figure shows that l is parallel to m and ∠ABC=60o, ∠BCD=30o, and ∠  [#permalink]

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Difficulty:   45% (medium)

Question Stats: 62% (01:59) correct 38% (02:22) wrong based on 26 sessions

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[GMAT math practice question] The figure shows that $$l$$ is parallel to $$m$$ and $$∠ABC=60^o, ∠BCD=30^o$$, and $$∠CDE=90^o$$. What is the measure of $$∠DEF$$?

$$A. 100^o$$

$$B. 110^o$$

$$C. 120^o$$

$$D. 130^o$$

$$E. 140^o$$

Attachment: fighre.png [ 17.55 KiB | Viewed 250 times ]

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Originally posted by MathRevolution on 17 Oct 2019, 18:22.
Last edited by Bunuel on 20 Oct 2019, 00:01, edited 2 times in total.
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Re: The figure shows that l is parallel to m and ∠ABC=60o, ∠BCD=30o, and ∠  [#permalink]

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MathRevolution wrote:
[GMAT math practice question]

The figure shows that $$l$$ is parallel to $$m$$ and $$∠ABC=60^o, ∠BCD=30^o$$, and $$∠CDE=90^o$$. What is the measure of $$∠DEF$$?

$$A. 100^o$$

$$B. 110^o$$

$$C. 120^o$$

$$D. 130^o$$

$$E. 140^o$$

Sorry! The figure is not visible.

Posted from my mobile device
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Re: The figure shows that l is parallel to m and ∠ABC=60o, ∠BCD=30o, and ∠  [#permalink]

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Figure is not visible.

Posted from my mobile device
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Re: The figure shows that l is parallel to m and ∠ABC=60o, ∠BCD=30o, and ∠  [#permalink]

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Bunuel, MathRevolution

Seems like figure is missing
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Resource: GMATPrep RCs With Solution
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8163
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: The figure shows that l is parallel to m and ∠ABC=60o, ∠BCD=30o, and ∠  [#permalink]

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=>

Attachment: 10.17ps(a).png [ 24.26 KiB | Viewed 219 times ]

We draw lines $$p$$ and $$q$$ parallel to $$l$$ and $$m.$$

When we put $$<DEF = <DHI = <x$$ and $$<GDC=<y,$$ we have $$<HDJ=<DHC=180°-x$$

Since we have $$<ABG=<GCD$$ and $$<GDC=<DCH$$, we have $$60°=30°+<y$$ and $$<y=30°.$$

Since $$<GDC+<CDH+<HDJ=180°$$ or $$<y+90°+180°-<x=180°$$, we have $$30°+270°-<x=180°, 300°-<x=180°$$ or $$<x = <DEF = 120°.$$

_________________ Re: The figure shows that l is parallel to m and ∠ABC=60o, ∠BCD=30o, and ∠   [#permalink] 20 Oct 2019, 19:13
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# The figure shows that l is parallel to m and ∠ABC=60o, ∠BCD=30o, and ∠  