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16 Sep 2014, 01:20
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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
A. 30 degrees
B. 50 degrees
C. 70 degrees
D. 100 degrees
E. 120 degrees
16 Sep 2014, 01:20
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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.
\(\angle ADC = \angle BDA + \angle BDC = \angle CBD + \angle ABD = \angle CBD + (180 - \angle BAD - \angle BDA) =\)
\(= 30 + (180 - 80 - 30) = 100\).
Answer: D
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
Joined: 12 Nov 2015
Last visit: 03 Jul 2017
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Location: Uruguay
Concentration: General Management
Schools: Goizueta '19 (A)
GMAT 1: 610 Q41 V32
GMAT 2: 620 Q45 V31
GMAT 3: 640 Q46 V32
GPA: 3.97
17 Apr 2016, 12:53
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To make the explanation visual, did someone solve this question graphically? thank you.
