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Question

Find the radian measure of the interior angle of a regular (i) Pentagon (ii) Hexagon (iii) Octagon

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Solution

Sum of interior angle of a regular polygon is (n2)π
so in (i) number of sides of pentagon are 5 thus n=5(52)π3π
Sum of all interior angles is 3π thus measure of each one is 3π5
(ii) Hexagon n=6(62)π=4π
Sum of all interior angles is 4π thus measure of each one is 4π5
(iii) Octagon n=8(82)π=6π
Sum of all interior angles is 6π thus measure of each one is 6π5

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