Each of these statements is giving you 2 of the 4 angles. With statement 1, you know that with 2 angles, the sum is 180, leaving you with 180 left for the other 2 angles. Nothing in the statement gives an indication as to the measure of either of those angles.
Statement 2 also only gives you 2 angles. You know that ABC is twice the measure of BCD. So it could be anything like ABC = 1 degree, BCD = 2, or any combination that keeps the ratio of 1:2. If it was 90:180, that leaves 360 - 270, or 90 degrees for the other 2 angles. It could be 30, 60, or 29, 61. We don't know enough.
The reason C is not correct is that Statement 1 doesn't tell us which angles are each 90 degrees. We have to be able to identify 3 of the 4 angles to know if 60 degrees is left for at least 1 of the angles as the question asks.
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.
The answer is E, but I don`t see how it isn`t C
The sum of the interior angles in a quadrilateral would be 360; this is derived from the equation (4-2)(180).
If two angles are right angles (90 degrees each) that leaves 180 for the other two angles. If one angle is double the other that leaves 60 and 120 (60 + 120 = 180).
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.