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# M24-08

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Math Expert
Joined: 02 Sep 2009
Posts: 43804

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16 Sep 2014, 00:20
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Difficulty:

45% (medium)

Question Stats:

73% (01:57) correct 27% (02:25) wrong based on 41 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
[Reveal] Spoiler: OA

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Math Expert
Joined: 02 Sep 2009
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16 Sep 2014, 00:20
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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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17 Apr 2016, 11:53
To make the explanation visual, did someone solve this question graphically? thank you.
Intern
Joined: 27 Mar 2014
Posts: 9

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16 Aug 2016, 17:52
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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Manager
Joined: 26 Jan 2016
Posts: 115
Location: United States
GPA: 3.37

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27 Nov 2016, 18:32
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...
Current Student
Joined: 12 Jul 2013
Posts: 7

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07 Dec 2016, 20:45
Hi Bunnel,

Can you please elaborate more on solution .. i got this question wrong.
Manager
Joined: 03 Jan 2016
Posts: 60
Location: India
WE: Engineering (Energy and Utilities)

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05 Apr 2017, 00:55
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
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Joined: 02 Sep 2009
Posts: 43804

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05 Apr 2017, 01:08
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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10 May 2017, 21:53
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

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11 May 2017, 01:23
Here is the image for visual view
Attachment:
Capture.PNG

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11 May 2017, 01:42
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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Re: M24-08   [#permalink] 11 May 2017, 01:42
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# M24-08

Moderators: chetan2u, Bunuel

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