Question
A regular polygon is having 4p+2 as the number of its
sides where p is a positive integer. What will be the ratio of the measure of its interior angle to that of its exterior angle?Solution
Interior angle of a polygon = [ ( n - 2 ) π ] / n = [ ( 4p + 2 - 2 ) π ] / ( 4p + 2 ) = ( 4p × π ) / ( 4p + 2 ) Exterior angle of a polygon = 2π / n = 2π/(4p + 2) The ratio of the interior angle of the polygon to the exterior angle of the polygon is, (4p × π)/(4p + 2) : 2π /(4p + 2) = ( 4p × π ) : 2π = 2p : 1
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