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

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For the cube shown above, what is the degree measure of PQR [#permalink] New post 02 Feb 2005, 21:35
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Attachment:
cube.gif
cube.gif [ 2.13 KiB | Viewed 5454 times ]
For the cube shown above, what is the degree measure of PQR?

A. 30
B. 45
C. 60
D. 75
E. 90
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Jun 2012, 06:40, edited 1 time in total.
Edited the question and added the OA.
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 [#permalink] New post 02 Feb 2005, 22:03
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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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 [#permalink] New post 03 Feb 2005, 05:46
actually the reasning i took was all the diagonals that make the triangle are = as they are formd from the same = sides hence 60
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 [#permalink] New post 03 Feb 2005, 07:24
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60 for the triangle being equilateral...all diagonals r equal
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 [#permalink] New post 03 Feb 2005, 07:28
I cannot see the figure. Can anybody tell me how do I do that.
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Re: For the cube shown above, what is the degree measure of [#permalink] New post 30 Jun 2012, 06:34
Hi, I understood the answer and I agree, but I can't find out why my logic isn't right.

Since it's a cube, all angles are 90 degrees, and since PO and RO are the bisectrix of the angle 90, than PQR would have to be 90, which is not the answer. What am thinking wrong?

Thanks.
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Re: For the cube shown above, what is the degree measure of [#permalink] New post 30 Jun 2012, 06:43
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ferrarih wrote:
Hi, I understood the answer and I agree, but I can't find out why my logic isn't right.

Since it's a cube, all angles are 90 degrees, and since PO and RO are the bisectrix of the angle 90, than PQR would have to be 90, which is not the answer. What am thinking wrong?

Thanks.


Below solution might help.

For the cube shown above, what is the degree measure of PQR?
A. 30
B. 45
C. 60
D. 75
E. 90
Attachment:
cube.gif
cube.gif [ 2.28 KiB | Viewed 4801 times ]
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 02 Oct 2013, 13:54
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Re: For the cube shown above, what is the degree measure of PQR [#permalink] New post 28 Oct 2013, 21:18
What if the given figure was cuboid?
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Re: For the cube shown above, what is the degree measure of PQR [#permalink] New post 28 Oct 2013, 22:49
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Re: For the cube shown above, what is the degree measure of PQR [#permalink] New post 23 May 2014, 10:38
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 23 May 2014, 11:22
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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 997 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 998 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 23 May 2014, 11:24
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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:
Attachment:
squares.png
squares.png [ 1.8 KiB | Viewed 994 times ]


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, 15:16
Yeah,Thank you very much.It helps me to understand the concept of diagonals in cube.
Re: For the cube shown above, what is the degree measure of PQR   [#permalink] 23 May 2014, 15:16
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