Interior angles of a quadrilateral

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Interior angles of a quadrilateral

by rafodr » Wed Sep 16, 2009 9:06 am
I dont understand this one... please help!

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

My reasoning:
(1) is not sufficient cause you could have more than one combination of angles, such as:
90 90 60 120
90 90 45 135
(2) is not sufficient cause it does not tell you anything about the other two angles

I think the answer is C, but GMATPrep says that the answer is E. How could this be??
Source: — Data Sufficiency |

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rafodr wrote:I dont understand this one... please help!

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

My reasoning:
(1) is not sufficient cause you could have more than one combination of angles, such as:
90 90 60 120
90 90 45 135
(2) is not sufficient cause it does not tell you anything about the other two angles

I think the answer is C, but GMATPrep says that the answer is E. How could this be??
We can see that the answer is E by examining two conflicting sets of angles in the quadrilateral (that still adhere to the conditions set out in statements 1 and 2)
Angles:
90 90 60 120 (one angle does equal 60)
45 90 90 135 (no angles equal 60)
Brent Hanneson - Creator of GMATPrepNow.com
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