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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]

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24 Oct 2005, 20:20
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85% (hard)

Question Stats:

42% (01:56) correct 58% (01:08) wrong based on 257 sessions

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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.

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-the-measure-of-one-of-the-interior-angles-of-127226.html
[Reveal] Spoiler: OA

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-Vikram

Last edited by Bunuel on 27 Jul 2014, 15:02, edited 1 time in total.
Edited the question and added the OA.
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Re: Is the measure of one of the interior angles of [#permalink]

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24 Oct 2005, 20:50
E

ABCD = 90/90/45/135
ABCD = 90/120/60/90
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Re: Is the measure of one of the interior angles of [#permalink]

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24 Oct 2005, 21:03
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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: Is the measure of one of the interior angles of [#permalink]

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25 Oct 2005, 02:13
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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Re: Is the measure of one of the interior angles of [#permalink]

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25 Oct 2005, 08:05
MBAQST explained it best. The answer must be E.
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Re: Is the measure of one of the interior angles of [#permalink]

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27 Jul 2014, 09:33
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Re: Is the measure of one of the interior angles of [#permalink]

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27 Jul 2014, 15:03
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Is the measure of one of the interior angles of quadrilateral ABCD equal to 60?

Sum of inner angels of quadrilateral is 360 degrees. (Sum of inner angles of polygon=180*(n-2), where n is # of sides)

(1) Two of the interior angles of ABCD are right angles --> angles can be 90+90 + any combination of two angels totaling 180. Not sufficient.

(2) The degree measure of angle ABC is twice the degree measure of angle BCD --> <ABC=2<BCD. Not sufficient

(1)+(2) Angles can be 90+90+45+135 Or 90+90+60+120. Not sufficient.

OPEN DISCUSSION OF THIS QUESTION IS HERE: is-the-measure-of-one-of-the-interior-angles-of-127226.html
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Re: Is the measure of one of the interior angles of   [#permalink] 27 Jul 2014, 15:03
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