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Math Expert V
Joined: 02 Sep 2009
Posts: 59236

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Difficulty:   65% (hard)

Question Stats: 68% (01:39) correct 32% (01:54) wrong based on 168 sessions

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In quadrilateral $$ABCD$$, $$AB = CD$$ and $$BC = AD$$. If $$\angle CBD = 30$$ degrees and $$\angle BAD = 80$$ degrees, what is the value of $$\angle ADC$$?

A. 30 degrees
B. 50 degrees
C. 70 degrees
D. 100 degrees
E. 120 degrees

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Bunuel wrote:
In quadrilateral $$ABCD$$, $$AB = CD$$ and $$BC = AD$$. If $$\angle CBD = 30$$ degrees and $$\angle BAD = 80$$ degrees, what is the value of $$\angle ADC$$?

A. 30 degrees
B. 50 degrees
C. 70 degrees
D. 100 degrees
E. 120 degrees

Consecutive angles are supplementary => $$\angle BAD + \angle ADC=180$$

$$\angle ADC=180-80=100$$

Am I right here?
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Siva Rama Krishna Meka Retired Moderator V
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Here is the image for visual view
Attachment:
Capture.PNG

>> !!!

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Math Expert V
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bpdulog wrote:
Does the position of A, B , C and D matter for these types of problems? If we wanted to draw it, what is the correct placement?

Problem Solving
Figures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Data Sufficiency:
Figures:
• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
• Lines shown as straight are straight, and lines that appear jagged are also straight.
• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.
• All figures lie in a plane unless otherwise indicated.
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Math Expert V
Joined: 02 Sep 2009
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Official Solution:

In quadrilateral $$ABCD$$, $$AB = CD$$ and $$BC = AD$$. If $$\angle CBD = 30$$ degrees and $$\angle BAD = 80$$ degrees, what is the value of $$\angle ADC$$?

A. 30 degrees
B. 50 degrees
C. 70 degrees
D. 100 degrees
E. 120 degrees

Because $$AB = CD$$ and $$BC = AD$$, $$ABCD$$ is a parallelogram.

$$\angle ADC = \angle BDA + \angle BDC = \angle CBD + \angle ABD = \angle CBD + (180 - \angle BAD - \angle BDA) =$$

$$= 30 + (180 - 80 - 30) = 100$$.

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To make the explanation visual, did someone solve this question graphically? thank you.
Intern  Joined: 27 Mar 2014
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Hi Bunuel,

Thanks for all that you do. Your explanations have made the study grind a lot more manageable.

I was under the impression that when you write out an angle expression (ex. ∠ABC), it means the angle is formed by the intersection of line AB with line BC (see attached illustration)

Is this the case? If so, I'm having trouble visualizing how you could form the parallelogram above using the given information. Thanks in advance!
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Current Student B
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Can someone explain how B can be the vertex of angle CBD if the prompt states AB=CD and AD=BC? I can't figure out how to draw this...
Intern  B
Joined: 12 Jul 2013
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Hi Bunnel,

Can you please elaborate more on solution .. i got this question wrong.
Manager  S
Joined: 03 Jan 2016
Posts: 57
Location: India
WE: Engineering (Energy and Utilities)

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Question didn't mentioned that Opposite sides are parallel !!!!

can we still assume that given quadrilateral is Parallelogram?

Requesting expert analysis on this !!!

Narayana Raju
Math Expert V
Joined: 02 Sep 2009
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gvvsnraju@1 wrote:
Question didn't mentioned that Opposite sides are parallel !!!!

can we still assume that given quadrilateral is Parallelogram?

Requesting expert analysis on this !!!

Narayana Raju

This is explained in the solution:
Because $$AB = CD$$ and $$BC = AD$$, $$ABCD$$ is a parallelogram.

If two pairs of opposite sides of a quadrilateral are equal in length then the quadrilateral is a parallelogram.
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Math Expert V
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Sirakri wrote:
Bunuel wrote:
In quadrilateral $$ABCD$$, $$AB = CD$$ and $$BC = AD$$. If $$\angle CBD = 30$$ degrees and $$\angle BAD = 80$$ degrees, what is the value of $$\angle ADC$$?

A. 30 degrees
B. 50 degrees
C. 70 degrees
D. 100 degrees
E. 120 degrees

Consecutive angles are supplementary => $$\angle BAD + \angle ADC=180$$

$$\angle ADC=180-80=100$$

Am I right here?

Yes, consecutive angles in a parallelogram are supplementary, add to 180°, so yes you are right.
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Senior Manager  S
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+1 for option D. The angle is 100.
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Manager  B
Joined: 14 Aug 2012
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Location: United States
GMAT 1: 620 Q43 V33 GMAT 2: 690 Q47 V38 ### Show Tags

Does the position of A, B , C and D matter for these types of problems? If we wanted to draw it, what is the correct placement?
Intern  B
Joined: 02 Feb 2018
Posts: 31

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Because you know that its a parallelogram, you don't need the information that CBD is 30 degrees. Opposite angles in parallelogram are the same and quadrilateral has 360 degrees in total -> ADC = [360-(2*80)]/2
Intern  B
Joined: 11 Mar 2017
Posts: 11

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Hi,

I solved by simply deducting angle(BAD) from 180 degrees to find the supplementary angel of BAD, which will be equal to angle ADC since AB and DC are parallel.

Is this approach correct?

Bunuel wrote:
Official Solution:

In quadrilateral $$ABCD$$, $$AB = CD$$ and $$BC = AD$$. If $$\angle CBD = 30$$ degrees and $$\angle BAD = 80$$ degrees, what is the value of $$\angle ADC$$?

A. 30 degrees
B. 50 degrees
C. 70 degrees
D. 100 degrees
E. 120 degrees

Because $$AB = CD$$ and $$BC = AD$$, $$ABCD$$ is a parallelogram.

$$\angle ADC = \angle BDA + \angle BDC = \angle CBD + \angle ABD = \angle CBD + (180 - \angle BAD - \angle BDA) =$$

$$= 30 + (180 - 80 - 30) = 100$$. Re: M24-08   [#permalink] 06 Dec 2018, 22:19
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# M24-08

Moderators: chetan2u, Bunuel  