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

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

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New post 22 Apr 2017, 17:39
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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
216153.17.g500052img01.gif [ 1.09 KiB | Viewed 819 times ]


A) 180

B) 220

C) 240

D) 300

E) 360
[Reveal] Spoiler: OA

Last edited by Bunuel on 23 Apr 2017, 02:08, 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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New post 22 Apr 2017, 19:24
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



please follow fig below
x=180
y =120

x+y=300

Ans D
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216153.17.g500052img01.jpg
216153.17.g500052img01.jpg [ 10.88 KiB | Viewed 791 times ]

Senior Manager
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Joined: 26 Dec 2015
Posts: 286
Location: United States (CA)
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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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New post 23 Apr 2017, 10:08
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



please follow fig below
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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New post 23 Apr 2017, 10:55
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



please follow fig below
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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Re: In the figure attached, DE is parallel to FG and DG = EF. What is the [#permalink]

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New post 23 Apr 2017, 11:36
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
And answer 300


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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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New post 23 Apr 2017, 12:06
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
And answer 300


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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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New post 02 May 2017, 15:14
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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
ISOCELES TRAPEZOID.jpg [ 19.19 KiB | Viewed 608 times ]


To answer the question

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
x+y = 300 Answer D

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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In the figure attached, DE is parallel to FG and DG = EF. What is the   [#permalink] 02 May 2017, 15:14
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