M24-08

Question

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

Bunuel · Answer

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 .

Answer: D

Avigano · Answer

To make the explanation visual, did someone solve this question graphically? thank you.

dpgiii · Answer

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!

Joc456 · Answer

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...

rt1601 · Answer

Hi Bunnel,

Can you please elaborate more on solution .. i got this question wrong.

gvvsnraju@1 · Answer

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

can we still assume that given quadrilateral is Parallelogram?

Requesting expert analysis on this !!!

Thanks in advance

Narayana Raju

Bunuel · Answer

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.

Sirakri · Answer

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

\angle ADC=180-80=100

Am I right here?

broall · Answer

Here is the image for visual view Capture.PNG

Bunuel · Answer

Yes, consecutive angles in a parallelogram are supplementary, add to 180°, so yes you are right.

spetznaz · Answer

+1 for option D. The angle is 100.

bpdulog · Answer

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?

Bunuel · Answer

OFFICIAL GUIDE :

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.

barryseal · Answer

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 =  /2

bumpbot · Answer

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M24-08

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