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#1 2015-03-01 23:51:49

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,135

Need help with a polygon question

#1
A polygon has n sides. Given two of its interior angles are 161 degree and 125 degree while the other interior angles are each equal 158 degree. Find the value of n.


Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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#2 2015-03-01 23:59:44

ROA
Member
From: Nigeria
Registered: 2015-03-01
Posts: 5

Re: Need help with a polygon question

180(n-2) = 161+125 +158(n-2)

Therefore n=15


It is not the problem that matters but the courage you bring into solving it.

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#3 2015-03-02 01:15:59

bob bundy
Administrator
Registered: 2010-06-20
Posts: 8,137

Re: Need help with a polygon question

hi Chris,

At each vertex of any polygon there is an interior angle and an exterior angle.  The acute* angle between the two sides is the exterior one, and the obtuse angle is the interior one.

They add up to 180.

So for an n sided polygon the total of all these angles is 180n.

If you imagine a little ant walking around the perimeter of the polygon, each time it reaches a vertex it has to turn through the acute angle to carry on the walk along the next side.  After it has completed the walk it has turned a total of 360.  So the sum of the externals is 360 (true for all polygons). 
Therefore the sum of the internals is 180n - 360 = 180(n-2)

eg.  For a triangle, n = 3 , so the internals add to 180(3-2) = 180

For a quadrilateral, n = 4, so sum = 180(4-2) = 360

hexagon, n = 6, sum = 180(6-2) = 180 x 4 = 720.

and so on.

Bob

* If the polygon has 5 or more sides.  For n = 3 and 4, reverse acute and obtuse.


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

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#4 2015-03-02 01:58:43

David
Member
From: Bumpkinland
Registered: 2014-04-23
Posts: 3,135

Re: Need help with a polygon question

Thanks for the explanation guys!
Chris


Meaningless, meaningless, Everything is meaningless! - Ecclesiastes 1:2

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