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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]

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02 Feb 2005, 22:35
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 30 Jun 2012, 07:40, edited 1 time in total.
Edited the question and added the OA.
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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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03 Feb 2005, 06:46
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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03 Feb 2005, 08:24
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60 for the triangle being equilateral...all diagonals r equal
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03 Feb 2005, 08:28
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]

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30 Jun 2012, 07:34
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]

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30 Jun 2012, 07:43
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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 [ 2.28 KiB | Viewed 14123 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.

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Re: For the cube shown above, what is the degree measure of PQR [#permalink]

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02 Oct 2013, 14:54
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Re: For the cube shown above, what is the degree measure of PQR [#permalink]

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28 Oct 2013, 22:18
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]

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28 Oct 2013, 23:49
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What if the given figure was cuboid?

It would depend on the type of that cuboid.
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Re: For the cube shown above, what is the degree measure of PQR [#permalink]

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23 May 2014, 11:38
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]

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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 [ 17.85 KiB | Viewed 10309 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 [ 11.18 KiB | Viewed 10299 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]

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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:
Attachment:

squares.png [ 1.8 KiB | Viewed 10297 times ]

Does this make sense?
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Re: For the cube shown above, what is the degree measure of PQR [#permalink]

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

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14 Sep 2014, 04:23
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i am still not able to figure out ..why is it not 90 deg.

keeping in view the above figure..gmatacequants fig.

cant we say.
since sides are equal..ap=ar
in traingle apo..ap=ao(sides of cube)
thus, ap=ao (isos tr)
this implies ..angle apo=aop=45
similarly, ang. aor=45
thus, por= 90

wats wrong in this..
plz help
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Re: For the cube shown above, what is the degree measure of PQR [#permalink]

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14 Sep 2014, 16:24
Expert's post
shreygupta3192 wrote:
i am still not able to figure out ..why is it not 90 deg.

keeping in view the above figure..gmatacequants fig.

cant we say.
since sides are equal..ap=ar
in traingle apo..ap=ao(sides of cube)
thus, ap=ao (isos tr)
this implies ..angle apo=aop=45
similarly, ang. aor=45
thus, por= 90

wats wrong in this..
plz help

That's wrong because angle POR is not the sum of AOP and AOR. Please check here: for-the-cube-shown-above-what-is-the-degree-measure-of-pqr-13841.html#p1367597
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Re: For the cube shown above, what is the degree measure of PQR [#permalink]

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14 Sep 2014, 17:46
got it. thanku.
if i look from inside the cube..then yeah..its clear.
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Re: For the cube shown above, what is the degree measure of PQR [#permalink]

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14 Sep 2014, 17:57
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Re: For the cube shown above, what is the degree measure of PQR [#permalink]

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21 Sep 2015, 13:42
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For the cube shown above, what is the degree measure [#permalink]

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20 Apr 2016, 16:52
For the cube shown above, what is the degree measure of \PQR?

1) 30
2) 45
3) 60
4) 75
5) 90
For the cube shown above, what is the degree measure   [#permalink] 20 Apr 2016, 16:52

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