Official Solution:


Statement (1) by itself is sufficient. \(\angle AEB = 180 - 2*\angle EDC = 150^o\).

Statement (2) by itself is sufficient. \(\angle AEB = 180 - 2*\angle BAC = 180 - 2*(180 - 90 - \angle ACB) = 150^o\).


Answer: D
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The problem says it's a rectangle. A rectangle's diagonals bisect each other and are equal in length, so if you draw a rectangle and draw in the diagonals, you'll get 4 isosceles triangles. Both statements give one angle of the two angles between the base and the equal sides, so you can calculate the third angle from both statements and get to AEB.

+1 for D. Use the property that diagonals of a rectangle bisect one another. Both statements are sufficient individually. Hence option D.
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For (1). First of all, \(\angle AEB = \angle DEC\). Next, DEC is isosceles, thus \(\angle EDC = \angle ECD=15^o\). The sum of the angles in a triangle is 180 degrees:

\(\angle EDC + \angle ECD + \angle DEC = 180^o\);

\(\angle EDC + \angle EDC + \angle AEB = 180^o\);

\(\angle AEB = 180 - 2*\angle EDC = 150^o\).


For (2). First of all, \(\angle BAC + \angle ACB= 90^o\) --> \(\angle BAC =90^o-\angle ACB\). Next, AEB is isosceles, thus \(\angle BAC = \angle ABE\). The sum of the angles in a triangle is 180 degrees. \(\angle BAC + \angle ABE + \angle AEB = 180^o\);

\(\angle BAC + \angle BAC + \angle AEB = 180^o\);

\(\angle AEB =180^o-2*\angle BAC = 180^o-2*(90^o-\angle ACB)\)
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Resources:
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Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
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