kadishmj wrote: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 90 degrees
(2) The degree measure of angle ABC is twice the degree measure of BCD


OA is E (statements 1 and 2 together are insufficient).

I thought that the answer should have been 1. If two of the interior angles are 90 degrees, doesn't that mean that the other 2 angles HAVE to be 90 degrees? I don't see how they couldn't be. What am I missing?

Answer is E

As 1 tells ur about 2 angles….rest two can be of any measure….so not sufficient
2nd tells measure of ABC=2 measure of BCD……..dont know about rest of the angles

Combining both….will still not conclude which angles are 90 .

Are u sure OA is E

as if we combine the two statements then we have

a) two angles measure 90 degrees (so other 2 must be 180 degrees combined)

b) ABC=2 X measure of BCD

Now if BCD is one amongst the angles in stmt 1 i.e. 90 deg

then ABC = 2 X 90 =180 deg Not possible

hence we can say that BCD cannot be 90 deg (it is one
amongst the 2 angles which are not 90 degs)

hence we can say that BCD+2BCD (ABC) = 180

i.e. 3BCD =180

BCD =60 deg

hence SUFF

ans should be C

pls check this

I am quite agree with samirpandeyit62. Pls recheck it and let us know.

Waiting for ur reply!!!

Correct me if I am wrong

kadishmj wrote: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 90 degrees
(2) The degree measure of angle ABC is twice the degree measure of BCD

The answer is E.

1) if the angles are opposite, then its a rectangle or square. If angles are adjacent, then the other 2 angles could be any figure totalling to 180. INSUFF

2) INSUFF

Combining the two, if we assume that angle B is 90, then angle C is 45. then A will be 90 and D will be 135. So no angle is equal to 60.
But if you assume that angle B is 120, then angle C is 60. The other two adjacent angles will be 90 and 90. So 1 angle is 60.
So together is INSUFF

Thanks Ratin for the explanation, such things will help broaden everyone's thinking spectrum.

and mine too

Can anyone provide a methodical approach to this question?