GMAT CLUB TEST m18 - question 15

Hi,

Consider the rectangle ABCD (BC>AD) in the doc attached.
Given facts: angle ABD = 2 * angle EAD
Since diagonals of a rectangle are equal and bisect each other, we have EA=ED. Implying angle EAD = EDA.
Lets consider angle EAD = angle EDA = x.
We already know all angles in a rectangle are 90. Therefore angle BAD = 90
Considering the triangle BAD, sum of angles in a triangle is 180.
So, angle BAD + angle ABD + angle BDA = 180
90 + 2x + x = 180 => 3x = 90 => X = 30
Now, angle EDC = 90-30 = 60
Consider triangle ACD, again angle CAD + angle ADC + angle DCA = 180
30 + 90 +angle DCA = 180 = > angle DCA =60
Knowing 2 angles of triangle EDC to be 60, makes it a equilateral triangle, hence angle CED =60.

Hope its not confusing!