Official Solution:In rectangle \(ABCD\), \(E\) is the point of intersection of diagonals. If angle \(ABD\) is twice angle \(EAD\), what is the value of angle \(CED\)?
A. 30 degrees
B. 45 degrees
C. 60 degrees
D. 90 degrees
E. 120 degrees
Look at the diagram below:
Notice that since \(\angle{BAD}=90\) degrees then \(\angle{EAB}=90-x\) degrees.
Next, since diagonals of a rectangle are equal and bisect each other then \(AE=BE\). So, \(\angle{EAB}=\angle{EBA}\): \(90-x=2x\), which gives \(x=30\). Thus, \(\angle{EAB}=\angle{EBA}=60\) and \(\angle {AEB}=60\) degrees.
Finally as \(\angle{AEB}=\angle{CED}\) then \(\angle{CED}=60\) degrees.
Answer: C
Aren't the diagonals of a rectangle an angular bisector ? AS, WE KNOW THAT DE = BE. So, angle a should have each angle = 45 degree ? angle DAE = angle BAE = 45 ?
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55% (01:31) correct 
