Equal to 60?

[alex.gellatly]

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

OA is E, but I got C.... can someone please explain?
Thanks

[tutorphd]

Statements (1) and (2) together, give two different possible scenarios:

a) ABC is not one of the right angles -> ABC + BCD =180, ABC = 2BCD -> ABC = 120, BCD = 60 -> YES

b) ABC is one of the right angles -> BCD = 45 -> Sum of the other two angles is 360-90-45=225, one of them is 90 and the other is 135 -> NO

Since we get sometimes YES, sometimes NO, that is not sufficient.

[Birottam Dutta]

SO, here we understand that both are individually insufficient so we have to check for both statements together.

here we can have two cases, that either ABC is one of the right angles or it is not.

If it is not, then angle ABC and angle BCD must measure a sum of 180 which makes angle ABC 120* and angle BCD 60*.

But if angle ABc is one of he right angles = 90*, then angle BCD is 45*.

The other two angles are then 90* (the second of the right angles) and 360*- (90+90+45) = 135*.

So, we see that there is a case when one angle may not be 60*.

So, both statements are also not sufficient.

Hence, E!

[Anurag@Gurome]

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

OA is E, but I got C.... can someone please explain?
Thanks

Sum of interior angels of a quadrilateral is 360 degrees.

(1) Two of the interior angles of ABCD are right angles implies the angles can be 90 + 90 + the remaining two angles that sum up 180.
No definite answer; NOT sufficient.

(2) The degree measure of angle ABC is twice the degree measure of angle BCD implies angle ABC = 2 * angle BCD.
No definite answer; NOT sufficient.

Combining (1) and (2), the angles can be 90 + 90 + 45 + 135 = 360 OR 90 + 90 + 60 + 120.
No definite answer; NOT sufficient.

The correct answer is E.