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angles of a quadrilateral

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angles of a quadrilateral

by mkhanna » Thu Sep 24, 2009 8:33 am
Is the measure of one of interior angles of the 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.
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by ssmiles08 » Thu Sep 24, 2009 10:37 am
let x + y + z + v = 360 (sum of all angles in a quad)

1) Insufficient. Two right angles will give you 360-180 = 180. if x and y were right angles, z + v = 180. one of the angles does not have to be 60 degrees.

2) Insufficient. x = 2y. that still leaves us with 2y + y + z + v = 360

Together, there are still 2 possibilities:

First possibility:

x + y = 180

z = 2v = 180 + 3v = 360

v = 180/3 = 60

Second possibility:

x = 90; y = 90; x = 2z (z =45) v = 135

one of the angles is not 60 degrees here.

Insufficient

Therefore IMO (E)
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by grockit_jake » Thu Sep 24, 2009 3:40 pm
Yes, you may have thought "since you can't have an angles 2x90 = 180, then the only option is 60 and 120 for the remaining 180".

But either of right angles can serve as the doubled piece, leaving 90 90 45 and 135
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