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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,137

A polygon has n sides. Given one of its interior angles is 126° while the other interior angles are each equal to 162°. Calculate the number of sides of the polygon.

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

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Do you know the relation between polygons and their interior angle sum?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,137

Yes. Interior + Exterior = 180°

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

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

Hi David,

It seems you don't understand the polygon of a thing yet.

Just as we explained to you last time, the sum of interior angles of any polygon is 180n - 360 .

Which simplified to 180(n - 2) .

Now to your question,

126 + { ( n - 1 ) * 162 } = 180(n - 2) .

Solve above equation to get n which is is the number of sides of the polygon .

ROA

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

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David wrote:

Yes. Interior + Exterior = 180°

That is true but not the thing we want right now.

Do you know why what ROA claims is true?

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**David****Member**- From: Bumpkinland
- Registered: 2014-04-23
- Posts: 3,137

Nope.

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

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**bob bundy****Administrator**- Registered: 2010-06-20
- Posts: 8,366

hi David,

If a polygon has 'n' sides and interior + exterior = 180 at each vertex then

total interior + total exterior = 180n

The total exterior is always 360 for any polygon. (Imagine taking a 'walk' around the perimeter. At each vertex you have to turn one exterior angle to continue along the next side. By the time you have turned for every vertex you are back where you started and have turned through 360.)

So total interior + 360 = 180n => total interior = 180n - 360 = 180 (n-2)

Bob

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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