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One exterior angle of a regular polygon measures 10°. What is the measure of each interior angle? How many sides does the polygon have?
The interior angles of the regular polygon would each have a measure of ##170^o## The polygon would have 36 sides.
The interior and exterior angles of a polygon form a linear pair and are therefore supplementary with a sum of ##180^o##?
If the exterior angle of polygon is ##10^o## then the interior angle must be ##170^o##.
In order to find the value of the interior angle of a regular polygon the equation is ##((n-2)180)/n## where n is the number of sides of the regular polygon.
Given that the interior angle is ##170^o## we can plug in the value into the formula ##170 = ((n-2)180)/n## ##170n = 180n-360## ##-10n = -360## ##n = 36## Therefore the polygon has 36 sides.
