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 ) ฯ ] / nย = [ ( 4p + 2 - 2 ) ฯ ] / ( 4p + 2 ) = ( 4p ร ฯ ) / ( 4p + 2 ) Exterior angle of a polygon = 2ฯ / n = 2ฯ/(4p + 2) The ratio of the interior angle of the polygon to the exterior angle of the polygon is, (4p ร ฯ)/(4p + 2) :ย 2ฯ /(4p + 2) = ( 4p ร ฯ ) : 2ฯย = 2p : 1
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