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Is the measure of one of the interior angles of

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Is the measure of one of the interior angles of [#permalink] New post 24 Oct 2005, 19:20
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A
B
C
D
E

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100% (01:02) correct 0% (00:00) wrong based on 16 sessions
Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees?
1) Two of the internal 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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 [#permalink] New post 24 Oct 2005, 19:50
E

ABCD = 90/90/45/135
ABCD = 90/120/60/90
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 [#permalink] New post 24 Oct 2005, 20:03
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I got E.

1) Total internal measure is 360; two are right angles meaning the other two angles sum is 180
60+120=180
10+170=180
NOT SUFF => BCE

2) internal angles would be: x, 2x, y, z
Nothing is known about y, z and therefore we can have
30, 60, 100, 170
40, 80, 120, 120
etc.
NOT SUFF => CE

1+2) taken together the internal angles can be:
x, 2x, 90, 90 (60, 120, 90, 90)
x, 2x, 90, 135 (45, 90, 90, 135)
NOT SUFF => E
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Re: DS: Quadrilateral [#permalink] New post 25 Oct 2005, 01:13
vikramm wrote:
Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees?
1) Two of the internal angles of ABCD are right angles
2) The degree measure of angle ABC is twice the degree measure of angle BCD.


I've got to agree with the posters saying E.

1) is clearly insufficient
2) by itself is clearly insufficient

Taken together the statements are still insufficient. ABC could be one of the 90 degree angles, or it could be a 120 degree angle. Thus, BCD could be either 45 or 60 degrees.
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 [#permalink] New post 25 Oct 2005, 07:05
MBAQST explained it best. The answer must be E.
  [#permalink] 25 Oct 2005, 07:05
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