SOLUTION: The measure of each interior angle of a regular polygon is 20 degrees more than three times the measure of each exterior angle. How many sides does the polygon have?

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Question 821048: The measure of each interior angle of a regular polygon is 20 degrees more than three times the measure of each exterior angle. How many sides does the polygon have?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
The exterior and interior angles of a polygon come in exterior-interior supplementary pairs.

So, if each exterior angle measures x degrees,
the measure of each interior angle, in degrees, is 180-x .

"The measure of each interior angle of a regular polygon is 20 degrees more than three times the measure of each exterior angle" translates into the equation
180-x=3x%2B20
From that equation we find x .
180-x=3x%2B20
180=x%2B3x%2B20
180=4x%2B20
180-20=4x
160=4x
160%2F4=x
x=40
Each exterior angle measures 40%5Eo .

The measures of the exterior angles of a polygon add up to 360%5Eo because the exterior angle is the angle we turn at each corner (vertex) as we go around the polygon, and one turn around is going full circle, meaning 360%5Eo .
If the regular polygon has n sides, the sum of the equal 40%5Eo measures of the n angles is
n%2A40%5Eo=360%5Eo , so
n=360%5Eo%2F40%5Eo
highlight%28n=9%29
The polygon has highlight%289%29 sides.