Question

What is the minimum interior angle in degrees possible for a regular polygon?

• A. $45$
• B. $55$
• C. $60$
• D. $65$

Answer 1

Answer: (C)

$60$

Let there be an $n$ sided polygon.

It is known that the sum of the interior angles of an $n$ sided polygon is

$S=(n-2)\times {180}^o.$

$S$ will have least positive integral value, which is $>0$

$(n-2)=1⟹n=3.$

$\therefore$ It is a triangle.

But it is a regular polygon, so the triangle is equiangular.

i.e One interior angle is ${60}^o$