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Is the measure of one of the interior angles of quadrilateral ABCD

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Is the measure of one of the interior angles of quadrilateral ABCD [#permalink] New post 30 May 2008, 05:21
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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:
The answer is E, but I don`t see how it isn`t C

The sum of the interior angles in a quadrilateral would be 360; this is derived from the equation (4-2)(180).
If two angles are right angles (90 degrees each) that leaves 180 for the other two angles. If one angle is double the other that leaves 60 and 120 (60 + 120 = 180).
[Reveal] Spoiler: OA
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Re: Is the measure of one of the interior angles of quadrilateral ABCD [#permalink] New post 30 May 2008, 07:19
Each of these statements is giving you 2 of the 4 angles. With statement 1, you know that with 2 angles, the sum is 180, leaving you with 180 left for the other 2 angles. Nothing in the statement gives an indication as to the measure of either of those angles.

Statement 2 also only gives you 2 angles. You know that ABC is twice the measure of BCD. So it could be anything like ABC = 1 degree, BCD = 2, or any combination that keeps the ratio of 1:2. If it was 90:180, that leaves 360 - 270, or 90 degrees for the other 2 angles. It could be 30, 60, or 29, 61. We don't know enough.

The reason C is not correct is that Statement 1 doesn't tell us which angles are each 90 degrees. We have to be able to identify 3 of the 4 angles to know if 60 degrees is left for at least 1 of the angles as the question asks.

japped187 wrote:
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.

The answer is E, but I don`t see how it isn`t C

The sum of the interior angles in a quadrilateral would be 360; this is derived from the equation (4-2)(180).
If two angles are right angles (90 degrees each) that leaves 180 for the other two angles. If one angle is double the other that leaves 60 and 120 (60 + 120 = 180).

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Re: Is the measure of one of the interior angles of quadrilateral ABCD [#permalink] New post 30 May 2008, 07:25
What if one angle is 45 degrees, which is double of 90 degrees? You are not given that it is only remaining two angles other than right angles which are fulfilling the statement 2.
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Re: Is the measure of one of the interior angles of quadrilateral ABCD [#permalink] New post 30 May 2008, 07:35
abhijit_sen wrote:
What if one angle is 45 degrees, which is double of 90 degrees? You are not given that it is only remaining two angles other than right angles which are fulfilling the statement 2.

Yes. That is correct.
The question only says ABC=2BCD.
What if angle ABC is one of the right angles.
The question doesn't mention and we can't assume.
Hence, E

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Re: Is the measure of one of the interior angles of quadrilateral ABCD [#permalink] New post 04 Jun 2011, 10:50
It is good trap question, I chose somehow that other two are 90 and 90 which automatically meant the required angle is 60

While I should have considered any angle could be 90 and other could be 45 etc..

Hence answer is E
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Re: Is the measure of one of the interior angles of quadrilateral ABCD [#permalink] New post 04 Jun 2011, 18:40
Trapped ! Went for C but then got the correct explanations !
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Re: Is the measure of one of the interior angles of quadrilateral ABCD [#permalink] New post 05 Jun 2011, 16:24
E, Good question. Need to be careful.
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Re: Is the measure of one of the interior angles of quadrilateral ABCD [#permalink] New post 05 Jun 2011, 23:21
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angles can be 90,90,60 and 120 or 90,45,90,and 135.

Hence E.
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Re: Is the measure of one of the interior angles of quadrilateral ABCD [#permalink] New post 25 Aug 2015, 11:00
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Re: Is the measure of one of the interior angles of [#permalink] New post 25 Aug 2015, 22:48
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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.

Answer: E.

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] 25 Aug 2015, 22:48
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