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# In the figure attached, DE is parallel to FG and DG = EF. What is the

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Manager
Joined: 26 Dec 2015
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Location: United States (CA)
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In the figure attached, DE is parallel to FG and DG = EF. What is the  [#permalink]

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Updated on: 23 Apr 2017, 03:08
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In the figure attached, DE is parallel to FG and DG = EF. What is the value of x+y?
Attachment:

216153.17.g500052img01.gif [ 1.09 KiB | Viewed 2048 times ]

A) 180

B) 220

C) 240

D) 300

E) 360

Originally posted by LakerFan24 on 22 Apr 2017, 18:39.
Last edited by Bunuel on 23 Apr 2017, 03:08, edited 1 time in total.
Renamed the topic.
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Re: In the figure attached, DE is parallel to FG and DG = EF. What is the  [#permalink]

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22 Apr 2017, 20:24
LakerFan24 wrote:
In the figure attached, DE is parallel to FG and DG = EF. What is the value of x+y?

A) 180

B) 220

C) 240

D) 300

E) 360

x=180
y =120

x+y=300

Ans D
Attachments

216153.17.g500052img01.jpg [ 10.88 KiB | Viewed 2014 times ]

Manager
Joined: 26 Dec 2015
Posts: 246
Location: United States (CA)
Concentration: Finance, Strategy
WE: Investment Banking (Venture Capital)
Re: In the figure attached, DE is parallel to FG and DG = EF. What is the  [#permalink]

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23 Apr 2017, 11:08
rohit8865 wrote:
LakerFan24 wrote:
In the figure attached, DE is parallel to FG and DG = EF. What is the value of x+y?

A) 180

B) 220

C) 240

D) 300

E) 360

x=180
y =120

x+y=300

Ans D

how did you know to put an equilateral triangle on top of the quadrilateral? is there another way of solving this?

also, isn't the sum of the angles within the quadrilateral 360 degrees? if x+y=300, doesn't that mean z+unknown angle = 60 degrees?
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Re: In the figure attached, DE is parallel to FG and DG = EF. What is the  [#permalink]

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23 Apr 2017, 11:55
LakerFan24 wrote:
rohit8865 wrote:
LakerFan24 wrote:
In the figure attached, DE is parallel to FG and DG = EF. What is the value of x+y?

A) 180

B) 220

C) 240

D) 300

E) 360

x=180
y =120

x+y=300

Ans D

how did you know to put an equilateral triangle on top of the quadrilateral? is there another way of solving this?

also, isn't the sum of the angles within the quadrilateral 360 degrees? if x+y=300, doesn't that meanz+unknown angle = 60 degrees?

I did so because only one angle value ie 120 is given....and one have to write all angles in terms of that 120 angle.
also if u analyze my solution ,u find easily the concept of 360 sum of quadrilateral ,which i used

for the 2nd highligted part ,please be more specific for unknown angles

thanks
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Joined: 13 Mar 2017
Posts: 2
Re: In the figure attached, DE is parallel to FG and DG = EF. What is the  [#permalink]

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23 Apr 2017, 12:36
1. Sum of internal a ngles of that quadrilateral is (n-2) 180° = 360°; n - number of sides.
2. Z+120° = 180; hence z 60.
3. Simple math y = 120°.
4. Z=x/3 & Y = unknown angle.
Thus x = 180

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Posts: 2609
Schools: Boston U '20 (M)
GRE 1: Q169 V154
Re: In the figure attached, DE is parallel to FG and DG = EF. What is the  [#permalink]

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23 Apr 2017, 13:06
rajeevysr wrote:
1. Sum of internal a ngles of that quadrilateral is (n-2) 180° = 360°; n - number of sides.
2. Z+120° = 180; hence z 60.
3. Simple math y = 120°.
4. Z=x/3 & Y = unknown angle.
Thus x = 180

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∂o you ,mind explaining the highlighted part.
How did you get to it without putting a equilateral triangle on top as rohit8865

Excellent solution rohit8865

Kudos.!

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In the figure attached, DE is parallel to FG and DG = EF. What is the  [#permalink]

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02 May 2017, 16:14
1
1
LakerFan24 wrote:
In the figure attached, DE is parallel to FG and DG = EF. What is the value of x+y?

A) 180
B) 220
C) 240
D) 300
E) 360

Nice solutions, here . . .

But you don't need to draw a triangle.

The key is that DG = EF

It's an isosceles trapezoid.

You can derive y or z, and hence x, from the following properties (see diagram):

A - The lower base angles are congruent (here, G and F)

B - The upper base angles are congruent (here, D and E) - I didn't use this one, but if you were looking for angles that summed to 360, it would help quickly

C - Opposite angles are supplementary, i.e., sum to 180 ($$\frac{x}{3}$$ and y are supplementary)

D - Adjacent angles are also supplementary (y and z)

Attachment:

ISOCELES TRAPEZOID.jpg [ 19.19 KiB | Viewed 1830 times ]

1. Derive z from the straight line. 120 + z = 180, z = 60

2. Derive x. Angles G and z are congruent base angles, see C above. Angle G = $$\frac{x}{3}$$, so z = $$\frac{x}{3}$$ ==>

$$\frac{x}{3}$$= 60, x = 180.

3. Derive y EITHER

-- from interior angles property, see D above (if z is 60, y will be 120), y = 120 OR

-- from drawing extended lines, see diagram (120 and y are alternate interior angles of parallel lines cut by a transversal), y = 120

Solution

y = 120
x = 180

Hope that helps.

$$Note to self: READ the question. I didn't catch DG=EF until more than three minutes in, AND I didn't catch "x + y" and marked the wrong answer. Edited to add figure, edited again to simplify post!$$
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Re: In the figure attached, DE is parallel to FG and DG = EF. What is the  [#permalink]

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31 Aug 2018, 05:35
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Re: In the figure attached, DE is parallel to FG and DG = EF. What is the   [#permalink] 31 Aug 2018, 05:35
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