Math Is Fun Forum

David

Member

From: Bumpkinland

Registered: 2014-04-23

Posts: 3,164

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.

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His dominion is an everlasting dominion, Which shall not pass away, And His kingdom the one Which shall not be destroyed.

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

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

Bob

Administrator

Registered: 2010-06-20

Posts: 10,143

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.

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Children are not defined by school ...........The Fonz
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David

Member

From: Bumpkinland

Registered: 2014-04-23

Posts: 3,164

Re: Need help with a polygon question

Thanks for the explanation guys!
Chris

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His dominion is an everlasting dominion, Which shall not pass away, And His kingdom the one Which shall not be destroyed.