Math Is Fun Forum

mathstudent2000

Member

Registered: 2013-07-26

Posts: 79

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

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Genius is one percent inspiration and ninety-nine percent perspiration

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathstudent2000

Member

Registered: 2013-07-26

Posts: 79

Re: rotation problem

ok so is \theta 144 degrees?

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Genius is one percent inspiration and ninety-nine percent perspiration

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: rotation problem

Yes, well done. 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathstudent2000

Member

Registered: 2013-07-26

Posts: 79

Re: rotation problem

but its wrong

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Genius is one percent inspiration and ninety-nine percent perspiration

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

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

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

mathstudent2000

Member

Registered: 2013-07-26

Posts: 79

Re: rotation problem

so its 72?

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Genius is one percent inspiration and ninety-nine percent perspiration

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: rotation problem

Well I hope so.  Fingers crossed this time. 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob