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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 [#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?

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 18002 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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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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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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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 14157 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.

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:

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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..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

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

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

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21 Sep 2015, 13:42

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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