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$1.)$ What is the minimum measure of exterior angle possible for a regular polygon. $2.)$ What is the maximum measure of interior angle possible for a regular polygon.? $3.)$ And how many sides could that polygon have ?

The maximum exterior angle possible for a regular polygon is $120^{\circ}$.

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And minimum interior angle possible for a regular polygon is $60^{\circ}$.

which are both in cases of equilateral triangle.

so i hope the for the question $1.)$ and $2.)$would be $\approx 0.01^{\circ}$ and $\approx 179.99^{\circ}$.

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For a regular polygon of $n$ sides ($n>3$) the exterior angle is $360/n$. This attains a maximum at $n=3$ and is always positive. The infimum is zero and the minimum value is never attained. For an non-rigorous, elementary proof of the latter result, suppose the minimum is $0.01$ (for general case take $x>0$), if I take $n= 360/0.01 +1$, then $360/n < 0.01$.

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