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# What is the measure of the angle made by the diagonals of th

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What is the measure of the angle made by the diagonals of th [#permalink]

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29 Dec 2009, 04:39
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What is the measure of the angle made by the diagonals of the any adjacent sides of a cube.

A. 30
B. 45
C. 60
D. 75
E. 90
[Reveal] Spoiler: OA
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29 Dec 2009, 06:17
C.. 60 degrees

All the diagonals are equal. If we take 3 touching sides and connect their diagonals, we form an equilateral Triangle. Therefore, each angle would be 60.

Any other method?
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29 Dec 2009, 06:50
aknine wrote:
xcusemeplz2009 wrote:
imo its 45

sorry my bad i was wrng in understanding the Q,
you are right its 60
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29 Dec 2009, 06:55
could anyone please explain in detail??
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29 Dec 2009, 10:49
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sagarsabnis wrote:
could anyone please explain in detail??

Take the diagonals of adjacent sides of a cube, so that they make an angle.

Join the ends of these diagonals to get the triangle.

You'll see that the line segment joining the ends of these diagonals will also be the diagonal of a side of a cube.

Hence we have the triangle all 3 sides of which are diagonals of a side of a cube. All diagonals are equal, which means that we have equilateral triangle. Any angle in equilateral triangle is 60 degrees.

Hope it's clear.
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04 Jan 2010, 00:20
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Re: What is the measure of the angle made by the diagonals of th [#permalink]

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18 Jun 2014, 11:51
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Re: What is the measure of the angle made by the diagonals of th [#permalink]

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18 Jun 2014, 12:55
Bunuel wrote:
sagarsabnis wrote:
could anyone please explain in detail??

Take the diagonals of adjacent sides of a cube, so that they make an angle.

Join the ends of these diagonals to get the triangle.

You'll see that the line segment joining the ends of these diagonals will also be the diagonal of a side of a cube.

Hence we have the triangle all 3 sides of which are diagonals of a side of a cube. All diagonals are equal, which means that we have equilateral triangle. Any angle in equilateral triangle is 60 degrees.

Hope it's clear.

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Re: What is the measure of the angle made by the diagonals of th [#permalink]

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19 Jun 2014, 01:29
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The triangle formed is equilateral

Refer diagram below:
Attachments

sq.jpg [ 36.25 KiB | Viewed 1761 times ]

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Re: What is the measure of the angle made by the diagonals of th [#permalink]

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24 Oct 2015, 23:13
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Re: What is the measure of the angle made by the diagonals of th [#permalink]

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28 Oct 2016, 04:01
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Re: What is the measure of the angle made by the diagonals of th   [#permalink] 28 Oct 2016, 04:01
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