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**mathstudent2000****Member**- Registered: 2013-07-26
- Posts: 79

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 (2013-08-10 08:01:26)*

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**bob bundy****Moderator**- Registered: 2010-06-20
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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

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**mathstudent2000****Member**- Registered: 2013-07-26
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ok so is \theta 144 degrees?

Genius is one percent inspiration and ninety-nine percent perspiration

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**bob bundy****Moderator**- Registered: 2010-06-20
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Yes, well done.

Bob

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

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**mathstudent2000****Member**- Registered: 2013-07-26
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but its wrong

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**bob bundy****Moderator**- Registered: 2010-06-20
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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

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Bob

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

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**mathstudent2000****Member**- Registered: 2013-07-26
- Posts: 79

so its 72?

Genius is one percent inspiration and ninety-nine percent perspiration

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**bob bundy****Moderator**- Registered: 2010-06-20
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Well I hope so. Fingers crossed this time.

Bob

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