Bunuel wrote:

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

(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.

Please share your way of thinking, not only post the answers.

OA and explanations to follow.

Option 1 we know 2 angles are 90 degree each but we have no info about the other 2 angles which can be (60,120), (80,100) etc. hence insuff

Option 2 says angle ABC = 2 * angle BCD again insuff as we can have an angle equal to 60 degree or none of the angles as 60degree

Taking 1 and 2 we know 2 angles are 90degree each and angle ABC is twice angle BCD

lets assume angle ABC = 90 degree then angle BCD = 45. we know the 3rd angle is 90 degree so 4th angle becomes 135 (sum of angles of a quadrilateral = 360degrees) so answer will NO ( none of angles are 60degree)

now lets consider that the 1st unknown angle is twice the 2nd unknown angle (other 2 are 90 degree each) we can get value for smaller angle as 60degree

hence insuff

will go with E

Asterix

from eeek?? to Eureka!!! to eeek???

One angle is x other is 2x, x+2x =180(360-180), this gives x = 60 degree....B is correct...