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) (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 degrees,
the measure of each interior angle, in degrees, is .
"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
From that equation we find .
Each exterior angle measures .
The measures of the exterior angles of a polygon add up to 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 .
If the regular polygon has sides, the sum of the equal measures of the angles is
, so
The polygon has sides.
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