Angles of quarilateral

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Nailya: Senior | Next Rank: 100 Posts; Posts: 91; Joined: Sat Feb 21, 2009 3:46 pm; Location: New York City; Thanked: 2 times

Angles of quarilateral

by Nailya » Fri Apr 10, 2009 9:17 am

Is the measure of one of the 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 for angle BCD

OA is E but my answer is C!

Where is the trap?

Quote

Source: Beat The GMAT — Data Sufficiency | Fri Apr 10, 2009 9:17 am

relic: Junior | Next Rank: 30 Posts; Posts: 22; Joined: Tue Mar 31, 2009 5:28 am; Thanked: 3 times; GMAT Score:780

by relic » Fri Apr 10, 2009 9:35 am

Imagine a right trapezoid-- two adjacent angles are right. This shape can provide both an example of a 60 degree angle and a counterexample.

First, the example. Let's make angles DAB and CDA the right angles. Let's have BCD measure 60 degrees, leaving ABC to measure 120. Thus ABCD can have a 60 angle.

But it doesn't have to. For the counterexample, let's make DAB and ABC the right angles. If we make BCD 45 degrees, we've now satisfied both statement yet the quadrilateral has no 60 degree angle.

A quick sketch can definitely help.

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