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# Is the measure of one of the interior angles of

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Senior Manager
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Is the measure of one of the interior angles of [#permalink]

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19 Sep 2005, 19:33
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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

Last edited by Bunuel on 11 Sep 2013, 02:47, edited 1 time in total.
Edited the question and added the OA
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18 Dec 2005, 16:45
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ps_dahiya wrote:
It must be C.

S1: Sum of remaining two angles = 180 so those may be 110,70 or anything else. INSUFF.

S2: INSUFF just by common sense

Combined:

Sum of ABC and BCD = 360-180 (Two right angles from S1) = 180. Say BCD = x then ABC = 2x

S0 3x = 180 and x = 60. SUFF

I think your assumption is wrong. As pointed above the angles can be 90,90,45,135 also. Both conditions are met. Both conditions are not sufficient to conclusively answer. IMO answer is E.
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18 Dec 2005, 23:36
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prash_c wrote:
ps_dahiya wrote:
It must be C.

S1: Sum of remaining two angles = 180 so those may be 110,70 or anything else. INSUFF.

S2: INSUFF just by common sense

Combined:

Sum of ABC and BCD = 360-180 (Two right angles from S1) = 180. Say BCD = x then ABC = 2x

S0 3x = 180 and x = 60. SUFF

I think your assumption is wrong. As pointed above the angles can be 90,90,45,135 also. Both conditions are met. Both conditions are not sufficient to conclusively answer. IMO answer is E.

You are absolutely right. I thought on the wrong lines. It should be E.
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20 Mar 2006, 16:55
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Yeah I change my mind. It should be E
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20 Mar 2006, 20:28
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yeah i realised my mistake lately ... assumption .. assumption .. huff
God help me!!

Answer is E guys ... we have ratio and I commited a big mistake!!
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19 Sep 2005, 20:19
E

1 is insufficient because it only gives us info on two angles.

2 is insufficient because it only gives us info on two angles.

Combine and sufficient.

The two 90 degree angles have to cannot be part of statement two together but one of the 90 degree angles can be. If ABC = 90 than BCD = 45 and CDA = 145.

But if no 90 degree angle is included in statment two than one angle equals 120 and the other 60.
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19 Sep 2005, 20:24
E.
statement i not clear about the remaing angles could have any measurements.

statement ii is also not clear with respect to the iterior angles of the qudlterl.

Togather also it is not sufficient to have clear measure of the angles.
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19 Sep 2005, 20:40
E it is. Agree with the reasoning!
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19 Sep 2005, 21:22
Never mind, I see where I went wrong.

I assumed that the two 90-degree angles had to be opposites, because if they were adjacent I falsely assumed the quadrilateral would have to be a rectangle, because it would form two parallel lines. Of course, I realize now that these two parallel lines could be of different lengths, so the pair of angles where one is double the other could not involve a 90 degree angle at all.

Anyway, I see now that it's E. Thanks for clearing it up.
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20 Sep 2005, 04:41
Hallo everybody, i think that both together are sufficient to answer the question if one of the interior angles is equal to 60 degrees.
From A) we know that 2 of the angles are right. We can select these in 6 ways
From B) we know that two adjacent angles ABC and BCD are in ratio- ABC/BCD= 2/1
Now by A) and B) by any comb of 2 angles that are right we can find info about the other angles and establish if there is an angle that is 60 degrees
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15 Dec 2005, 02:52
I agree with BG, I think it shud be C!
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16 Dec 2005, 05:02
C

S1: Sum of remaining two angles = 180 so those may be 110,70 or anything else. INSUFF.

S2: INSUFF just by common sense

Combined:

Sum of ABC and BCD = 360-180 (Two right angles from S1) = 180. Say BCD = x then ABC = 2x

S0 3x = 180 and x = 60. SUFF
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Last edited by ps_dahiya on 18 Dec 2005, 23:37, edited 1 time in total.
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19 Dec 2005, 17:38
here is an illustration
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20 Mar 2006, 20:25

4 variables

1st option gives value of 2
2nd relation between missing two ... and their sum is 4(90) deg.
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20 Mar 2006, 20:31
This is my first post.

C is the correct answer because the second statements states that a certain angle (say A) is twice the other angle (say B).

So angle 45 and 145 are impossible.

1) Statement : two angle are 90deg
Conclusion: Sum of other two angles 180deg

2) Angle A twice Angle B
Therefore A+B=180
or B+2B=180 --> B=60
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20 Mar 2006, 20:35
How can 135deg angle be twice the 45 deg angle ?
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21 Mar 2006, 05:42
This is my first post.

C is the correct answer because the second statements states that a certain angle (say A) is twice the other angle (say B).

So angle 45 and 145 are impossible.

1) Statement : two angle are 90deg
Conclusion: Sum of other two angles 180deg

2) Angle A twice Angle B
Therefore A+B=180
or B+2B=180 --> B=60

Angle A twice Angle B
If ABC=90, BCD=ABC/2=45, CDA=135, DAC=90.

So 45 and 135 is not impossible.
In your assumption in 2), you consider only one possibility, that one right angle cannot be considered as the double of the other.
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Re: Is the measure of one of the interior angles of [#permalink]

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10 Sep 2013, 12:20
This is an old thread but need to restart this one to get the correct ans.
IMO ans is E but seeing some replies in this thread i am confused btw C &E.
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Re: Is the measure of one of the interior angles of [#permalink]

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11 Sep 2013, 02:48
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Phoenix72 wrote:
This is an old thread but need to restart this one to get the correct ans.
IMO ans is E but seeing some replies in this thread i am confused btw C &E.

The correct answer is indeed E.

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] 11 Sep 2013, 02:48
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