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## #1 2013-08-11 06:00:35

mathstudent2000
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### rotation problem

OPQRSTUVWX is a regular decagon. A rotation of \theta degrees about U maps X to R. Given \theta < 180 degrees, find \theta

Last edited by mathstudent2000 (2013-08-11 06:01:26)

Genius is one percent inspiration and ninety-nine percent perspiration

## #2 2013-08-11 06:18:55

bob bundy
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### Re: rotation problem

If you rotate just enough to move all the points on just one place, let's call the an angle of D degrees.

If you repeat D ten times you get back to where you started, so 10D = 360.

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #3 2013-08-11 06:24:56

mathstudent2000
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### Re: rotation problem

ok so is \theta 144 degrees?

Genius is one percent inspiration and ninety-nine percent perspiration

## #4 2013-08-11 06:45:10

bob bundy
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### Re: rotation problem

Yes, well done.

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #5 2013-08-12 02:48:17

mathstudent2000
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### Re: rotation problem

but its wrong

Genius is one percent inspiration and ninety-nine percent perspiration

## #6 2013-08-12 05:05:22

bob bundy
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### Re: rotation problem

Curious.  See diagram.  I should appeal that mark.

Hold a mo.  It says rotate about U.    I had assumed it was being rotated about the centre.  I'm having a rethink.

Rethink done.  Many apologies.  I didn't read the question properly.  I had assumed we were rotating around the centre of the decagon.  But the centre is U.  Refer to second diagram below.

The angle you want is XUR.

There's a theorem that the angle at the centre of a circle, XCR, is twice the angle at the edge, XUR.

http://www.mathisfunforum.com/viewtopic.php?id=17799

post 6

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

## #7 2013-08-12 09:18:39

mathstudent2000
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### Re: rotation problem

so its 72?

Genius is one percent inspiration and ninety-nine percent perspiration

## #8 2013-08-12 16:57:31

bob bundy
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### Re: rotation problem

Well I hope so.  Fingers crossed this time.

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei