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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 07 Feb 2012, 17:01
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

45% (01:59) correct 55% (00:57) wrong based on 66 sessions
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

[Reveal] Spoiler:
As the OA is not given, I have gone for answer C and this is how I reached. Please let me know whether I am right.

First, we know that the sum of 4 angles of a quadrilateral is 360 degrees.

Now, considering statement 1

Two angles are right angles. Not sufficient as it doesn't say anything about the other two angles.

Considering Statement 2

Not sufficient as it doesn't say anything about the other two angles.

Combining both statements

We can find the 4th angle as below

90+90+90+x = 360
270+x = 360
x = 90. where x is the 4th angle. So the answer is NO the angle won't be 60 degrees.
[Reveal] Spoiler: OA

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Last edited by Bunuel on 17 Sep 2012, 23:48, edited 3 times in total.
Edited the OA
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Re: Quadrilateral ABCD [#permalink] New post 07 Feb 2012, 17:07
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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.
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Re: Is the measure of one of the interior angles of [#permalink] New post 07 Feb 2012, 22:25
That question was a tricky sucker.
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Trignometry [#permalink] New post 17 Sep 2012, 20:35
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.

A. Statement (1) ALONEis sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONEis sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHERare sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

My approach to the problem :

Each statement individually cannot help solve the question. Using combined information from two statements:

It isn't clear from combined information whether angle BCD is right angle. So two cases arises here.

Case 1: If angle BCD is not the a right angle. In this case Angle ABC is 60 degrees since ABC + BCD = 180 degress as sum of other two angles of quadrilateral is 180 degress.

Case 2: If angle BCD is the right angle. In this case angle ABC is 45 degrees and other angles of quadrilateral are 90 and 135 degrees.

So we cannot clearly say that angle ABC is 60 with both information combined and so my answer to this is E but the official answer is otherwise.

Please correct if my logic is incorrect.
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Re: Trignometry [#permalink] New post 17 Sep 2012, 23:50
Expert's post
dineesha 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.

A. Statement (1) ALONEis sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONEis sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHERare sufficient, but NEITHER statement ALONE is sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.

My approach to the problem :

Each statement individually cannot help solve the question. Using combined information from two statements:

It isn't clear from combined information whether angle BCD is right angle. So two cases arises here.

Case 1: If angle BCD is not the a right angle. In this case Angle ABC is 60 degrees since ABC + BCD = 180 degress as sum of other two angles of quadrilateral is 180 degress.

Case 2: If angle BCD is the right angle. In this case angle ABC is 45 degrees and other angles of quadrilateral are 90 and 135 degrees.

So we cannot clearly say that angle ABC is 60 with both information combined and so my answer to this is E but the official answer is otherwise.

Please correct if my logic is incorrect.


Merging similar topics. please refer to the solution above.

P.S. Please read carefully and follow: rules-for-posting-please-read-this-before-posting-133935.html
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Re: Is the measure of one of the interior angles of [#permalink] New post 06 Oct 2012, 05:30
Since two angles of the quad. are right angles, would other angles not be right angles as well? As sides emanating from right angles would only be straight, and hence the corresponding angles will also be right angles? Correct me if I am wrong. Thx.
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Re: Is the measure of one of the interior angles of [#permalink] New post 06 Oct 2012, 05:49
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chigiwigi wrote:
Since two angles of the quad. are right angles, would other angles not be right angles as well? As sides emanating from right angles would only be straight, and hence the corresponding angles will also be right angles? Correct me if I am wrong. Thx.


Consider the diagram below:
Attachment:
Trapezoid.png
Trapezoid.png [ 1.62 KiB | Viewed 1828 times ]
As you can see we can have a quadrilateral with only two right angles.

Hope it helps.
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RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
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Re: Is the measure of one of the interior angles of [#permalink] New post 06 Oct 2012, 06:31
ok, makes sense. Thanks.
Re: Is the measure of one of the interior angles of   [#permalink] 06 Oct 2012, 06:31
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