Question 1194423
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Definition: A regular polygon has all sides equal to one another. Also, the angles are equal to one another.


Examples:<ul><li>An equilateral triangle is a regular polygon with 3 equal sides of any length of your choosing. Each angle is 60 degrees.</li><li>A square is a regular polygon with 4 equal sides of your choosing. Each angle is 90 degrees.</li></ul>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: <font color=red>9 sides</font>


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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.
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