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M18-15
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16 Sep 2014, 01:03
16 Sep 2014, 01:03
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Difficulty:
75%
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Question Stats:
56% (02:22) correct
44%
(02:24)
wrong
based on 223
sessions
In rectangle \(ABCD\), point \(E\) is the intersection of the diagonals. If angle \(ABD\) is twice the size of angle \(EAD\), what is the measure of angle \(CED\)?
A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 90 degrees
E. 120 degrees
A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 90 degrees
E. 120 degrees
Re M18-15
[#permalink]
16 Sep 2014, 01:03
16 Sep 2014, 01:03
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4
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Expert Reply
Official Solution:
In rectangle \(ABCD\), point \(E\) is the intersection of the diagonals. If angle \(ABD\) is twice the size of angle \(EAD\), what is the measure of angle \(CED\)?
A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 90 degrees
E. 120 degrees
Refer to the diagram below:
Observe that since \(\angle BAD = 90\) degrees, then \(\angle EAB = 90 - x\) degrees.
Furthermore, since the diagonals of a rectangle are equal in length and bisect each other, we have \(AE = BE\). Consequently, \(\angle EAB = \angle EBA\). From this, we get \(90 - x = 2x\), which results in \(x = 30\). Thus, \(\angle EAB = \angle EBA = 60\) and \(\angle AEB = 60\) degrees.
Lastly, since \(\angle AEB = \angle CED\), we can conclude that \(\angle CED = 60\) degrees.
Answer: C
In rectangle \(ABCD\), point \(E\) is the intersection of the diagonals. If angle \(ABD\) is twice the size of angle \(EAD\), what is the measure of angle \(CED\)?
A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 90 degrees
E. 120 degrees
Refer to the diagram below:
Observe that since \(\angle BAD = 90\) degrees, then \(\angle EAB = 90 - x\) degrees.
Furthermore, since the diagonals of a rectangle are equal in length and bisect each other, we have \(AE = BE\). Consequently, \(\angle EAB = \angle EBA\). From this, we get \(90 - x = 2x\), which results in \(x = 30\). Thus, \(\angle EAB = \angle EBA = 60\) and \(\angle AEB = 60\) degrees.
Lastly, since \(\angle AEB = \angle CED\), we can conclude that \(\angle CED = 60\) degrees.
Answer: C
General Discussion
Target Test Prep Representative
Joined: 24 Nov 2014
Status:Chief Curriculum and Content Architect
Affiliations: Target Test Prep
Posts: 3480
Given Kudos: 1431
GMAT 1: 800 Q51 V51 
Re: M18-15
[#permalink]
03 Mar 2015, 05:44
03 Mar 2015, 05:44
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I think this question is good and helpful.
