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# The figure above is a cube. What is the measure of angle BEG

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The figure above is a cube. What is the measure of angle BEG [#permalink]

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26 Mar 2012, 06:25
Attachment:

Cube - Q.jpg [ 21.46 KiB | Viewed 6510 times ]
The figure above is a cube. What is the measure of angle BEG (not shown)?
A. 30°
B. 45°
C. 60°
D. 75°
E. 90°

Hi everyone,
I wanted to make you a quick and apparently easy question that it's giving me a hard time:

What is the angle formed by the diagonals of to perpendicular faces of a cube?

I know the answer but I can't visualize why that's the answer

Source: local GMAT course

Last edited by Bunuel on 26 Mar 2012, 07:36, edited 2 times in total.
Added a question, diagram and OA
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Re: Cube, Diagonals and Angles [#permalink]

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26 Mar 2012, 07:32
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htbreme wrote:
Hi everyone,
I wanted to make you a quick and apparently easy question that it's giving me a hard time:

What is the angle formed by the diagonals of to perpendicular faces of a cube?

I know the answer but I can't visualize why that's the answer

Source: local GMAT course

Attachment:

Cube.jpg [ 30.11 KiB | Viewed 6855 times ]
The figure above is a cube. What is the measure of angle BEG (not shown)?
A. 30°
B. 45°
C. 60°
D. 75°
E. 90°

Note that triangle BEG 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.

Hope it helps.
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Re: The figure above is a cube. What is the measure of angle BEG [#permalink]

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26 Mar 2012, 08:35
Thank you Bunuel, for the edit and for the answer. As the image provided in the exercise was not clear I was misinterpreting the angle that the question was asking to identify, this makes total sense now.

Thank again

Cheers
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Re: Cube, Diagonals and Angles [#permalink]

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31 Mar 2012, 11:16
Bunuel wrote:
htbreme wrote:
Hi everyone,
I wanted to make you a quick and apparently easy question that it's giving me a hard time:

What is the angle formed by the diagonals of to perpendicular faces of a cube?

I know the answer but I can't visualize why that's the answer

Source: local GMAT course

Attachment:
Cube.jpg
The figure above is a cube. What is the measure of angle BEG (not shown)?
A. 30°
B. 45°
C. 60°
D. 75°
E. 90°

Note that triangle BEG 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.

Hope it helps.

Why isn't it 90? Since two diagonals bisect two 90 degree angles would the x angle equal to 90? I understand your explanation, but would like to understand why my thinking is wrong? Thank you.
Math Expert
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Posts: 38908
Followers: 7740

Kudos [?]: 106262 [0], given: 11618

Re: Cube, Diagonals and Angles [#permalink]

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31 Mar 2012, 12:12
bohdan01 wrote:
Bunuel wrote:
htbreme wrote:
Hi everyone,
I wanted to make you a quick and apparently easy question that it's giving me a hard time:

What is the angle formed by the diagonals of to perpendicular faces of a cube?

I know the answer but I can't visualize why that's the answer

Source: local GMAT course

Attachment:
The attachment Cube.jpg is no longer available
The figure above is a cube. What is the measure of angle BEG (not shown)?
A. 30°
B. 45°
C. 60°
D. 75°
E. 90°

Note that triangle BEG 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.

Hope it helps.

Why isn't it 90? Since two diagonals bisect two 90 degree angles would the x angle equal to 90? I understand your explanation, but would like to understand why my thinking is wrong? Thank you.

It would be correct for 2-D geometry, meaning the angle between two diagonals below is indeed 90 degrees:
Attachment:

Squares.png [ 2.5 KiB | Viewed 6316 times ]
But in 3-D geometry 2 faces are already 90 degrees to each other thus their diagonals would not form 90 degrees any more.

Hope it's clear.
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Re: Cube, Diagonals and Angles [#permalink]

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31 Mar 2012, 13:25
htbreme wrote:
Hi everyone,
I wanted to make you a quick and apparently easy question that it's giving me a hard time:

What is the angle formed by the diagonals of to perpendicular faces of a cube?

I know the answer but I can't visualize why that's the answer

Source: local GMAT course

Unlike 2d shapes, 3d shapes cannot be viewed by plain eyes.
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Re: The figure above is a cube. What is the measure of angle BEG [#permalink]

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07 Oct 2016, 20:28
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Re: The figure above is a cube. What is the measure of angle BEG   [#permalink] 07 Oct 2016, 20:28
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