Is the measure of one of the interior angles of quadrilateral ABCD equal to 60?

Sum of inner angels of quadrilateral is 360 degrees. (Sum of inner angles of polygon=180*(n-2), where n is # of sides)

(1) Two of the interior angles of ABCD are right angles --> angles can be 90+90 + any combination of two angels totaling 180. Not sufficient.

(2) The degree measure of angle ABC is twice the degree measure of angle BCD --> <ABC=2<BCD. Not sufficient

(1)+(2) Angles can be 90+90+45+135 Or 90+90+60+120. Not sufficient.

Answer: E.
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Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees?
(1) Two of the interior angles of ABCD are right angles.
(2) The degree measure of angle ABC is twice the degree measure of angle BCD.

A. Statement (1) ALONEis sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONEis sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHERare sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

My approach to the problem :

Each statement individually cannot help solve the question. Using combined information from two statements:

It isn't clear from combined information whether angle BCD is right angle. So two cases arises here.

Case 1: If angle BCD is not the a right angle. In this case Angle ABC is 60 degrees since ABC + BCD = 180 degress as sum of other two angles of quadrilateral is 180 degress.

Case 2: If angle BCD is the right angle. In this case angle ABC is 45 degrees and other angles of quadrilateral are 90 and 135 degrees.

So we cannot clearly say that angle ABC is 60 with both information combined and so my answer to this is E but the official answer is otherwise.

Please correct if my logic is incorrect.

Since two angles of the quad. are right angles, would other angles not be right angles as well? As sides emanating from right angles would only be straight, and hence the corresponding angles will also be right angles? Correct me if I am wrong. Thx.

ok, makes sense. Thanks.