DS

[lionheart]

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).

[DaveGill]

E is the correct answer.
Both together:
The quadilateeral could have angles 90, 90, 45 and 135 degrees with angles ABC = 90 and BCD = 45.
or the angles could 90, 90, 120 and 60. with angle ABC = 120 and BCD = 60.
Hence insufficient.

[RonPurewal]

the flaw in your solution is found in the following line:

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).

unwarranted assumption.
you assumed that angles abc and bcd are not the right angles mentioned in statement (1), but there's no reason to make that assumption. angle abc could perfectly well be one of the 90 degree angles, creating the alternate set of degree measures (90/90/45/135) pointed out in the previous post.

this reminds me of an old grade school riddle about a girl, her mother, and her grandmother walking down the street together: 3 women, among whom are 2 mothers and 2 daughters. no contradiction there, as the girl's mother happens to be both.

[vinothdevakumar86]

@Ron, can yu explain this problem.

Is is possible to draw a quad with two 90 degree on the same side or opp side and still satisfy the condition angles on the same side sum upto 180?

I think it is not possible to get 60 with statement 1.
Hence A.

[RonPurewal]

@Ron, can yu explain this problem.

Is is possible to draw a quad with two 90 degree on the same side or opp side and still satisfy the condition angles on the same side sum upto 180?

I think it is not possible to get 60 with statement 1.
Hence A.

adjacent angles don't have to sum to 180 degrees, so there's the problem.

(in parallelograms they do, but nobody said this one had to be a parallelogram.)