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In the figure above, if angle ABC = 110 degrees, and angle AED = 100 d  [#permalink]

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Question Stats: 71% (00:18) correct 29% (01:08) wrong based on 7 sessions

### HideShow timer Statistics In the figure above, if angle ABC = 110 degrees, and angle AED = 100 degrees, then angle ADE is how many degrees smaller than angle BCD?

(1) Angle DAB = 45 degrees

(2) Angle ADC + angle BCD = 205 degrees

Hello. I am doing the PR1012, and I came across this question. I got it wrong to begin with, but I also do not understand their brief explanation. Please help me. Just for the record I am in the college class of 2015, but I need to take the GMAT before the end of my sophomore year for a combined degree program (shooting for 700; I know it is really hard!). Eventually I may want an MBA, though. I am studying now to ease into it. I am pretty smart for the most part, but I do badly on tests. I got a 1380 SAT (670M, 710CR) with a little studying. Anyway, here is the question.

After one day of studying I already hate the data questions. In the figure above, if angle ABC = 110 degrees, and angle AED = 100 degrees, then angle ADE is how many degrees smaller than angle BCD?

1. Angle DAB = 45 degrees

2. Angle ADC + angle BCD = 205 degrees

OPEN DISCUSSION OF THIS QUESTION IS HERE: this-ds-i-just-cannot-figure-out-i-am-getting-e-99063.html

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Originally posted by jw on 23 Jun 2011, 14:31.
Last edited by jw on 23 Jun 2011, 20:27, edited 1 time in total.
Senior Manager  Joined: 24 Mar 2011
Posts: 341
Location: Texas
Re: In the figure above, if angle ABC = 110 degrees, and angle AED = 100 d  [#permalink]

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st-2 is fairly simple to get BCD - ADE, so st is sufficient.

as per st -1, BCD = 360-110-100-45-DAE
BCD = 105-DAE

for triangle ADE, DAE = 180-100-ADE
DAE = 80-ADE

combining both eqns, BCD = 105-80+ADE
==> BCD - ADE = 25
sufficient.
Intern  Status: UF BSBA '15 - Preparing for the future
Joined: 09 May 2011
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Re: In the figure above, if angle ABC = 110 degrees, and angle AED = 100 d  [#permalink]

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My apologies for mis-posting.

Please move this to the data sufficiency forum.
Intern  Joined: 08 Mar 2011
Posts: 9
Re: In the figure above, if angle ABC = 110 degrees, and angle AED = 100 d  [#permalink]

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St 2 is very simple, as discussed in the above post. But I solved the first stmt like below, I hope it'll help you!
Let <BCD = y; <ADE = x; therefore <CDA = 180 - x (since, <CDA and <ADE are supplimentary)

Now sum of angles of quadrilateral ABCD is 360;
<DAB + <ABC + <BCD + <CDA = 360 => 45 + 110 + Y + 180 - X = 360

You can get the difference b/t y and X which is the answer for the question. Therefore the answer is D
Intern  Status: UF BSBA '15 - Preparing for the future
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GPA: 3.87
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Re: In the figure above, if angle ABC = 110 degrees, and angle AED = 100 d  [#permalink]

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I still do not see how statement two is so simple.
Retired Moderator Joined: 20 Dec 2010
Posts: 1772
Re: In the figure above, if angle ABC = 110 degrees, and angle AED = 100 d  [#permalink]

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jw wrote:
I still do not see how statement two is so simple.

Sum of angles in a straight line is 180.
ADE+ADC=180
ADC=180-ADE ------------1

2.
ADC + BCD = 205
Substitute ADC from 1
180-ADE+BCD=205
BCD-ADE=205-180=25

BCD-ADE is nothing but the difference asked in the question stem.
Sufficient.
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Posts: 55271
Re: In the figure above, if angle ABC = 110 degrees, and angle AED = 100 d  [#permalink]

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jw wrote: In the figure above, if angle ABC = 110 degrees, and angle AED = 100 degrees, then angle ADE is how many degrees smaller than angle BCD?

(1) Angle DAB = 45 degrees

(2) Angle ADC + angle BCD = 205 degrees

Hello. I am doing the PR1012, and I came across this question. I got it wrong to begin with, but I also do not understand their brief explanation. Please help me. Just for the record I am in the college class of 2015, but I need to take the GMAT before the end of my sophomore year for a combined degree program (shooting for 700; I know it is really hard!). Eventually I may want an MBA, though. I am studying now to ease into it. I am pretty smart for the most part, but I do badly on tests. I got a 1380 SAT (670M, 710CR) with a little studying. Anyway, here is the question.

After one day of studying I already hate the data questions. In the figure above, if angle ABC = 110 degrees, and angle AED = 100 degrees, then angle ADE is how many degrees smaller than angle BCD?

1. Angle DAB = 45 degrees

2. Angle ADC + angle BCD = 205 degrees

Important property of polygons: Sum of Interior Angles of a polygon is $$180(n-2)$$ where $$n$$ is the number of sides.

So for quadrilateral sum of the angles equals to $$180(4-2)=360$$ degrees. Given: $$\angle{ABC}=110$$ and $$\angle{AED}=100$$. Question: $$\angle{BCD}-\angle{ADE}=?$$.
Attachment:
DS.jpg
Now as $$\angle{ABC}=110$$ and $$\angle{AED}=100$$ and the sum of all angles is 360 degrees then the sum of other two angles in quadrilateral must be $$\angle{BCD}+\angle{BAE}=360-(110+100)=150$$.

(1) $$\angle{DAB}=45$$ --> $$\angle{BAE}=\angle{DAB}+\angle{DAE}=45+\angle{DAE}$$, but $$\angle{DAE}=180-100-\angle{ADE}=80-\angle{ADE}$$ (the sum of interior angles in triangle ADE equals to 180 degrees) --> $$\angle{BAE}=45+80-\angle{ADE}=125-\angle{ADE}$$. So $$\angle{BCD}+\angle{BAE}=150$$ becomes $$\angle{BCD}+125-\angle{ADE}=150$$ --> $$\angle{BCD}-\angle{ADE}=25$$. Sufficient.

(2) $$\angle{BCD}+\angle{ADC}=205$$ --> $$\angle{ADC}=180-\angle{ADE}$$ (straight line) --> $$\angle{BCD}+180-\angle{ADE}=205$$ --> $$\angle{BCD}-\angle{ADE}=25$$. Sufficient.

Answer: D.

OPEN DISCUSSION OF THIS QUESTION IS HERE: this-ds-i-just-cannot-figure-out-i-am-getting-e-99063.html

--== Message from the GMAT Club Team ==--

THERE IS LIKELY A BETTER DISCUSSION OF THIS EXACT QUESTION.
This discussion does not meet community quality standards. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________ Re: In the figure above, if angle ABC = 110 degrees, and angle AED = 100 d   [#permalink] 14 Aug 2017, 03:18
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# In the figure above, if angle ABC = 110 degrees, and angle AED = 100 d

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