SOLUTION: Here's the question from the book:"An interior angle of a regular polygon is given. Find the number of sides of the polygon. How do you find the number of sides?

Question 61248This question is from textbook
: Here's the question from the book:"An interior angle of a regular polygon is given. Find the number of sides of the polygon.
How do you find the number of sides? This question is from textbook

Answer by joyofmath(189) (Show Source): You can put this solution on YOUR website!
Here's the question from the book:"An interior angle of a regular polygon is given. Find the number of sides of the polygon.
A regular polygon has all sides the same and also all interior angles are the same.
A regular triangle has 3 internal angles that add up to 180 degrees.
A regular square has 4 internal angles that add up to 360 degrees.
A regular pentagon has 5 internal angles that add up to 540 degrees.
Every time you add a side to a polygon you add 180 degrees.
So, a 3-sided polygon has 1*180 degrees.
A 4-sided polygon has 2*180 degrees.
A 5-sided polygon has 3*180 degrees.
In general, an n-sided polygon has .
The interior angle of a regular n-sided polygon, call it I = .
So, if you know I and want to solve for n, you do the following algebra:
.
Multiply by n: .
Or, .
Subtract 180n from both sides: .
Factor out n:
Divide by I-180: .
Multiply numerator and denominator by -1: .
Verify the equation:
If I = 60 then A triangle!
If I = 90 then A square!
If I = 108 then A pentagon!
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