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Question

Is it possible to have a regular polygon whose each interior angle is :

(i) 170o

(ii) 138o


Solution

(i) No. of sides = n

each interior angle =170o

(n2)n×180o=170o180n360o=170n180n170n=360o10n=360on=360o10n=36

which is a whole number.

Hence it is possible to have a regular polygon

Whose interior angle is 170o

(ii) Let no. of sides =138o

(n2)n×180o=138o180n360o=138n180n138n=360o42n=360on=360o42n=60o7

which is not a whole number.

Hence it is not possible to have a regular polygon having interior angle of 138o.  

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