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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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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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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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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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60 for the triangle being equilateral...all diagonals r equal

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New post 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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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

Image

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.

[Reveal] Spoiler:
Attachment:
cube.gif
cube.gif [ 2.28 KiB | Viewed 31101 times ]

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What if the given figure was cuboid?

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New post 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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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 25606 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 25600 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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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 25591 times ]


Does this make sense?
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New post 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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i am still not able to figure out ..why is it not 90 deg.

keeping in view the above figure..gmatacequant`s fig.

can`t 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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New post 14 Sep 2014, 16:24
shreygupta3192 wrote:
i am still not able to figure out ..why is it not 90 deg.

keeping in view the above figure..gmatacequant`s fig.

can`t 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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New post 14 Sep 2014, 17:46
got it. thanku.
if i look from inside the cube..then yeah..its clear.

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got it. thanku.
if i look from inside the cube..then yeah..its clear.


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

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New post 17 Jul 2016, 01:13
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

Don't be in a hurry and say it is 90 degrees.
If you look closely , you will notice PQ and QR are two diagonals to the cube; therefore they will be equal in dimension. Now see If you join QR you will get another diagonal with.
NOW we get a triangle in which PQ=PR=RQ ; An equilateral triangle.

ALL angles of an equilateral triangle are 60 degrees.

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

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New post 25 Jul 2016, 01:50
Bunuel - What will be the value of each diagonal in the equilateral triangle that is formed here ? (triangle PQR)

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New post 25 Jul 2016, 01:56
Keats wrote:
Bunuel - What will be the value of each diagonal in the equilateral triangle that is formed here ? (triangle PQR)


Do you mean angles instead of diagonals? Triangle does not have diagonals. If you mean angles, then each angle in equilateral triangle is 60 degrees.
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Re: For the cube shown above, what is the degree measure of PQR [#permalink]

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New post 25 Jul 2016, 02:34
Bunuel wrote:
Keats wrote:
Bunuel - What will be the value of each diagonal in the equilateral triangle that is formed here ? (triangle PQR)


Do you mean angles instead of diagonals? Triangle does not have diagonals. If you mean angles, then each angle in equilateral triangle is 60 degrees.


Sorry that I didn't put it up correctly. I wanted to ask that what will be the value of each side of the equilateral triangle (which happens to be the diagonal of the cube), Bunuel

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Re: For the cube shown above, what is the degree measure of PQR   [#permalink] 25 Jul 2016, 02:34

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