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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] New post 26 Mar 2012, 05:25
Attachment:
Cube - Q.jpg
Cube - Q.jpg [ 21.46 KiB | Viewed 2451 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

Last edited by Bunuel on 26 Mar 2012, 06:36, edited 2 times in total.
Added a question, diagram and OA
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Re: Cube, Diagonals and Angles [#permalink] New post 26 Mar 2012, 06:32
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Expert's post
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
Cube.jpg [ 30.11 KiB | Viewed 2449 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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Re: The figure above is a cube. What is the measure of angle BEG [#permalink] New post 26 Mar 2012, 07:35
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

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Re: Cube, Diagonals and Angles [#permalink] New post 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

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.
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Re: Cube, Diagonals and Angles [#permalink] New post 31 Mar 2012, 11:12
Expert's post
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
Squares.png [ 2.5 KiB | Viewed 2266 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.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


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Re: Cube, Diagonals and Angles [#permalink] New post 31 Mar 2012, 12:25
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

Thanks in advance



Unlike 2d shapes, 3d shapes cannot be viewed by plain eyes. :-D
Re: Cube, Diagonals and Angles   [#permalink] 31 Mar 2012, 12:25
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