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The figure shows that l is parallel to m and ∠ABC=60o, ∠BCD=30o, and ∠

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MathRevolution
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The figure shows that l is parallel to m and ∠ABC=60o, ∠BCD=30o, and ∠ [#permalink] New post   Updated on: 20 Oct 2019, 00:01
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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 \(∠DEF\)?



\(A. 100^o\)

\(B. 110^o\)

\(C. 120^o\)

\(D. 130^o\)

\(E. 140^o\)


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C

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] New post   17 Oct 2019, 19:35
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.

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Re: The figure shows that l is parallel to m and ∠ABC=60o, ∠BCD=30o, and ∠ [#permalink] New post   17 Oct 2019, 20:16
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] New post   17 Oct 2019, 22:03
Bunuel, MathRevolution

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

Attachment:
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10.17ps(a).png [ 24.26 KiB | Viewed 1856 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 \(<x = <DEF = 120°.\)

Therefore, C is the answer.
Answer: C
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Re: The figure shows that l is parallel to m and ABC=60o, BCD=30o, and [#permalink] New post   29 Dec 2022, 15:09
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Re: The figure shows that l is parallel to m and ABC=60o, BCD=30o, and [#permalink]
29 Dec 2022, 15:09
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