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For the cube shown above, what is the degree measure of PQR

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nocilis
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For the cube shown above, what is the degree measure of PQR [#permalink] New post   Updated on: 10 Apr 2022, 05:11
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For the cube shown above, what is the degree measure of PQR?

A. 30
B. 45
C. 60
D. 75
E. 90

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cube.gif
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C

Originally posted by nocilis on 02 Feb 2005, 22:35.
Last edited by Sajjad1994 on 10 Apr 2022, 05:11, edited 2 times in total.
Edited the question and added the OA.
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Bunuel
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Re: For the cube shown above, what is the degree measure of PQR [#permalink] New post   30 Jun 2012, 07:43
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For the cube shown above, what is the degree measure of PQR?

A. 30
B. 45
C. 60
D. 75
E. 90



Note that triangle PQR is equilateral: it's made by the diagonals of the adjacent faces of the given cube (and as faces of a cube are squares its diagonals are equal). Thus angle BEG=60 degrees.

Answer: C.

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Re: For the cube shown above, what is the degree measure of PQR [#permalink] New post   23 May 2014, 12:22
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ankushbassi wrote:
Hi Bunuel, since the face of a cube forms the square and the diagonal of the square bisects the angles.The 2 diagonals shown in the pictures and each makes an angle of 45.Thus,why not the answer is 45+45=90?Can you please help me to understand this.

Hi Ankush,
The angle in question is as shown.Please refer the diagram below:
Attachment:
g2.png
g2.png [ 17.85 KiB | Viewed 99701 times ]

It would be an equilateral triangle made up by 3 face diagonals.


What you are referring are the two angles in two different planes.
which are angle POA and angle AOR each 45 degrees

They are on adjacent faces of the cube,which you cannot combine.
Attachment:
G5.png
G5.png [ 11.18 KiB | Viewed 99335 times ]


Hope this helps.
Press kudos if it was of help.


Kindly check the following post with the poll and revert with your replies
10-straight-lines-no-two-of-which-are-parallel-and-no-three-171525.html
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Re: For the cube shown above, what is the degree measure of PQR [#permalink] New post   02 Feb 2005, 23:03
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60 as well

because the figure in question is a cube sides pq,qr,pr are equal. Hence pqr is an equilateral triangle. So you get 60 for each included angle.
Had this been a cuboid, then it is a different story.
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Re: For the cube shown above, what is the degree measure of PQR [#permalink] New post   23 May 2014, 12:24
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ankushbassi wrote:
Hi Bunuel, since the face of a cube forms the square and the diagonal of the square bisects the angles.The 2 diagonals shown in the pictures and each makes an angle of 45.Thus,why not the answer is 45+45=90?Can you please help me to understand this.


Because these two squares are not in the same plane. If the square were in the same plane (as shown below), then you would be correct:



Does this make sense?


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Re: For the cube shown above, what is the degree measure of PQR [#permalink] New post   23 May 2014, 11:38
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Hi Bunuel, since the face of a cube forms the square and the diagonal of the square bisects the angles.The 2 diagonals shown in the pictures and each makes an angle of 45.Thus,why not the answer is 45+45=90?Can you please help me to understand this.
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Re: For the cube shown above, what is the degree measure of PQR [#permalink] New post   14 Sep 2014, 17:57
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Re: For the cube shown above, what is the degree measure of PQR [#permalink] New post   01 Aug 2016, 10:36
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nocilis wrote:
Attachment:
The attachment cube.gif is no longer available
For the cube shown above, what is the degree measure of PQR?

A. 30
B. 45
C. 60
D. 75
E. 90



Draw a construction (Pink Line) and

Answer: Option C
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File comment: www.GMATinsight.com
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Re: For the cube shown above, what is the degree measure of PQR [#permalink] New post   17 Dec 2019, 20:46
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nocilis wrote:
Attachment:
cube.gif
For the cube shown above, what is the degree measure of PQR?

A. 30
B. 45
C. 60
D. 75
E. 90


If we draw a line segment from P to R, we see that the length of PR = length of PQ = length of RQ, since each segment is the diagonal of a square face of the cube.

Thus, we have triangle PQR with all sides of equal lengths, and thus the degree measure of angle PQR is 60 degrees.

Answer: C
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Re: For the cube shown above, what is the degree measure of PQR [#permalink] New post   01 Feb 2023, 06:49
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