Problem Solving

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


A. 30
B. 45
C. 60
D. 75
E. 90


OA: C

PQR is an equilateral triangle formed by 3 diagonals of the cube.

Therefore, it would be 60 degrees

I picked 90 .. 45 + 45 - LOL

- pradeep

so what is the OA

I hope it must be 90

sudharsong wrote:I hope it must be 90

Dude no way .. it's 60

60 should be the ans

very interesting...

since the triangle is formed by the diagonals its an equilateral triangle so 60

but consider this reasoning too..

each triangle on the surface of the cube divides the side into 2. so the triangle would be 45-45-90
we have to add one more triangle to get the total angle.. that would be 45 +45 = 90.

Please let me know how to dispute the second line of reasoning..

shafeek wrote:very interesting...

since the triangle is formed by the diagonals its an equilateral triangle so 60

but consider this reasoning too..

each triangle on the surface of the cube divides the side into 2. so the triangle would be 45-45-90
we have to add one more triangle to get the total angle.. that would be 45 +45 = 90.

Please let me know how to dispute the second line of reasoning..

I dont understand, can you explain it? i end up in 90` because 45+45 but when is it 60?

Quite simple. each side of the triangle is a diagonal to the cube. Diagonals to the cube are equal in length. therefore the length of the sides of the triangle formed by joining the diagonals are equal in length.

Thus the triangle is equilateral. Since the triangle is equilateral, each angle is 60

Definitely 60. Maybe the key to this is to think of the triangle as a "slice" of the cube, rather than something that appears on each surface.

right it should be considered in the 3D.

For those who answer 90. You should consider this;
The angle will be 90 if you remove the two faces of the box and put them together on the same plain. But if you leave the box untouched, the angle will be 60 instead.

if one side of the cube is X

PR=PQ=QR= Xsqrt(2)

All sides are equal, hence 60