M18-15

Question

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

Bunuel · Accepted Answer

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:
 
 https://gmatclub.com/gmat-practice-tests/resources/import/img/m18-15.png 
 
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

MartyTargetTestPrep · Answer

I think this question is  good  and  helpful .

Senthil7 · Answer

I think this is a  high-quality  question and I agree with explanation.

19941010 · Answer

Hi,
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 ?
thanks

Bunuel · Answer

The diagonal of a rectangle is a bisector only if the rectangle is a square.

La1yaMalhotra · Answer

Aren't the diagonals of rectangle perpendicular bisector of each other?

Bunuel · Answer

The diagonals of a rectangle always bisect each other but they are perpendicular to each other only if a rectangle is a square.

spetznaz · Answer

The answer is option C. Well explained above.

culsivaji · Answer

I think this is a  high-quality  question and I agree with explanation.

vishalkss · Answer

Can you please explain the angle measure 2x for EBA

Gladiator59 · Answer

I think this is a  high-quality  question and I agree with explanation. Good & helpful.

dcummins · Answer

Good question.

I think what this brings to light are the rules of diagonals in a rectangle and the difference between the bisector of a rectangle and square.

"Each diagonal of a square is the perpendicular bisector of the other. That is, each cuts the other into two equal parts, and they cross and right angles (90°)"

Whereas, each diagonal of a rectangle bisects each other and divides the rectangle up into two equal parts, but the point at which the diagonals bisect does not create 4 equal angles.

Then, finding out what angle corresponds to what side can allow us to solve 90-x = 2x and so forth.

Thanks  Bunuel

RenanBragion · Answer

I think this is a  high-quality  question and I agree with explanation.

kri1311 · Answer

Great points in this question:

1. The diagonal of a rectangle is a bisector only if the rectangle is a square.
2. The diagonals of a rectangle always bisect each other but they are perpendicular to each other only if a rectangle is a square.

I made the mistake of assuming the diagonal as a bisector and selected the D option.

Great explanation with great information.

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

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