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

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

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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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,139

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

Thanks for the explanation guys!

Chris

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

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