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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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18 Jan 2012, 10:39
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Question Stats:

47% (00:51) correct 53% (01:10) wrong based on 345 sessions

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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°

Attachment:

Cube.jpg [ 21.46 KiB | Viewed 13449 times ]

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Posts: 62469
The figure above is a cube. What is the measure of angle BEG  [#permalink]

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18 Jan 2012, 10:47
5
4
Baten80 wrote:

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.

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

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Updated on: 11 Mar 2018, 10:11
Attachment:

Cube - Q.jpg [ 21.46 KiB | Viewed 14087 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

Originally posted by htbreme on 26 Mar 2012, 05:25.
Last edited by Bunuel on 11 Mar 2018, 10:11, edited 3 times in total.
Added a question, diagram and OA
Math Expert
Joined: 02 Sep 2009
Posts: 62469
Re: The figure above is a cube. What is the measure of angle BEG  [#permalink]

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26 Mar 2012, 06:32
3
1
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 15842 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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31 Mar 2012, 10:16
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
Joined: 02 Sep 2009
Posts: 62469
Re: The figure above is a cube. What is the measure of angle BEG  [#permalink]

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31 Mar 2012, 11:12
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 13861 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: The figure above is a cube. What is the measure of angle BEG  [#permalink]

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05 Nov 2016, 01:35
I don't understand this question. Where is there a triangle/an angle for BEG?

Posted from my mobile device
Math Expert
Joined: 02 Sep 2009
Posts: 62469
Re: The figure above is a cube. What is the measure of angle BEG  [#permalink]

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05 Nov 2016, 01:44
1
gillyelephant wrote:
I don't understand this question. Where is there a triangle/an angle for BEG?

Posted from my mobile device

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

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05 Nov 2016, 03:51
1
Baten80 wrote:
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°

Please find the solution as attached
Attachments

File comment: www.GMATinsight.com

Answer 3.jpg [ 58.96 KiB | Viewed 7660 times ]

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

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07 Nov 2016, 16:19
1
Baten80 wrote:
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°

Since our given figure is a cube, we must recall that a cube is made up of 6 squares, which of course have all equal sides. We need to determine the measure of angle BEG. Let’s draw that angle in a diagram:

From our diagram we can see that we can actually create a triangle using angle BEG with sides BE, EG, and GB. Notice that each side is the diagonal of a square face of the cube and thus is equal in length. Therefore, we know that triangle BEG is an equilateral triangle and furthermore that angle BEG is 60 degrees.

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

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29 Dec 2019, 16:17
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Re: The figure above is a cube. What is the measure of angle BEG   [#permalink] 29 Dec 2019, 16:17
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