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16 Sep 2014, 01:03
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C
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56% (02:22) correct
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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
16 Sep 2014, 01:03
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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
03 Mar 2015, 05:44
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I think this question is good and helpful.
