Problema Solution
The measure of each exterior angle of a regular polygon is 1/8 the measure of an interior angle. How many sides does the polygon have?
Answer provided by our tutors
Let 'x' represent the interior angle.
This mean the exterior angle can be written as x/8.
The interior and exterior angle add up to 180 degrees:
x + x/8 = 180
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click here to see the equation solved for x
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x = 160 angles
x/8 = 160/8 = 20 degrees
The exterior angles of a regular polygon add up to 360° thus each exterior equals 360/n, where n is the number of sides:
360/n = 20
n = 360/20
n = 18 sides
The polygon has 18 sides.