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Senior Manager  B
Status: No dream is too large, no dreamer is too small
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The figure above is a cube. What is the measure of angle BEG  [#permalink]

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16 00:00

Difficulty:   45% (medium)

Question Stats: 50% (00:53) correct 50% (01:11) wrong based on 429 sessions

### HideShow timer Statistics 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 10718 times ]

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Math Expert V
Joined: 02 Sep 2009
Posts: 55150
The figure above is a cube. What is the measure of angle BEG  [#permalink]

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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.

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

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Attachment: Cube - Q.jpg [ 21.46 KiB | Viewed 11691 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

Thanks in advance

Originally posted by htbreme on 26 Mar 2012, 06:25.
Last edited by Bunuel on 11 Mar 2018, 11:11, edited 3 times in total.
Added a question, diagram and OA
Math Expert V
Joined: 02 Sep 2009
Posts: 55150
Re: The figure above is a cube. What is the measure of angle BEG  [#permalink]

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2
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

Thanks in advance

Added a question about this issue for a better understating.

Attachment: Cube.jpg [ 30.11 KiB | Viewed 13147 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.

Answer: C.

Hope it helps.
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Joined: 30 Apr 2011
Posts: 12
Re: The figure above is a cube. What is the measure of angle BEG  [#permalink]

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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

Thanks in advance

Added a question about this issue for a better understating.

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.

Answer: C.

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 V
Joined: 02 Sep 2009
Posts: 55150
Re: The figure above is a cube. What is the measure of angle BEG  [#permalink]

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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

Thanks in advance

Added a question about this issue for a better understating.

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.

Answer: C.

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 11479 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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Joined: 08 Oct 2016
Posts: 49
Re: The figure above is a cube. What is the measure of angle BEG  [#permalink]

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I don't understand this question. Where is there a triangle/an angle for BEG?

Posted from my mobile device
Math Expert V
Joined: 02 Sep 2009
Posts: 55150
Re: The figure above is a cube. What is the measure of angle BEG  [#permalink]

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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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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 5268 times ]

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

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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.

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

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