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?

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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) About Me  (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 %28n-2%29%2A180+degrees.
The interior angle of a regular n-sided polygon, call it I = %28%28n-2%29%2A180%29%2Fn.
So, if you know I and want to solve for n, you do the following algebra:
I=%28%28n-2%29%2A180%29%2Fn.
Multiply by n: In=%28n-2%29%2A180%29.
Or, In=180n-360.
Subtract 180n from both sides: In-180n=-360.
Factor out n: n%28I-180%29=-360
Divide by I-180: n=-360%2F%28I-180%29.
Multiply numerator and denominator by -1: n=360%2F%28180-I%29.
Verify the equation:
If I = 60 then n=360%2F%28180-60%29+=+360%2F120+=+3 A triangle!
If I = 90 then n=360%2F%28180-90%29+=+360%2F90+=+4 A square!
If I = 108 then n=360%2F%28180-108%29+=+360%2F72+=+5 A pentagon!