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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

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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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.

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 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.

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:

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..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

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

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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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Posting an answer without an explanation is "GOD COMPLEX". The world doesn't need any more gods. Please explain you answers properly. FINAL GOODBYE :- 17th SEPTEMBER 2016. .. 16 March 2017 - I am back but for all purposes please consider me semi-retired.

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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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