SOLUTION: A regular pologon has it exterior angle being 100 degrees less than the interior angle,find the number of sides of the pologon.

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Question 1194423: A regular pologon has it exterior angle being 100 degrees less than the interior angle,find the number of sides of the pologon.
Found 3 solutions by math_tutor2020, Alan3354, MathTherapy:
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Definition: A regular polygon has all sides equal to one another. Also, the angles are equal to one another.

Examples:n = number of sides of the regular polygon
i = interior angle
E = exterior angle

We're told that "exterior angle being 100 degrees less than the interior angle", so,
Exterior angle = (interior angle) - 100
E = i - 100

If a regular polygon has n sides, then the interior angle (i) can be determined through this formula
i = 180(n-2)/n

The exterior angle (E) can be determined like so
E = 360/n

Apply substitution and solve for n.
E = i - 100
360/n = 180(n-2)/n - 100
360 = 180(n-2) - 100n
360 = 180n-360 - 100n
360 = 80n-360
360+360 = 80n
720 = 80n
n = 720/80
n = 9
This regular polygon has 9 sides.
This is a regular nonagon.
Note: in step 3, I multiplied both sides by n to clear out the denominators.

If this regular polygon has 9 sides, then,
E = 360/n = 360/9 = 40 degrees
i = 180(n-2)/n = 180(9-2)/9 = 140 degrees
We can see those values satisfy E = i - 100 to help confirm the answer.

Answer: 9 sides

------------------------------------------
Edit:

I'm realizing there's an alternative method
E = i - 100 is one equation we can form
i+E = 180 is another equation

Apply substitution and solve
i+E = 180
i+i-100 = 180
2i-100 = 180
2i = 180+100
2i = 280
i = 280/2
i = 140
and
E = i - 100
E = 140-100
E = 40
Then we can say
n = 360/E = 360/40 = 9
There are 9 sides to the polygon.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
A regular pologon [sic] has it exterior angle being 100 degrees less than the interior angle, find the number of sides of the pologon [sic].
===============
polygon, not pologon
------------
Ext + Int = 180 degs
(180 - 100)/2 = 40 degs (exterior angles)
360/40 = 9 sides
Answer by MathTherapy(10556)   (Show Source): You can put this solution on YOUR website!
A regular pologon polygon has it exterior angle being 100 degrees less than the interior angle, find the number of sides of the pologon.
With each exterior angle being E, each interior angle is then 180 - E 

We then get: E = 180 - E - 100

E + E = 180 - 100

2E = 80

Each exterior angle, or 

With sum of all exterior angles of ANY polygon being 360, and number of sides n, we get: 

, which translates to:  

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