Question

What is the maximum exterior angle in degrees possible for a polygon?

• A. $110$
• B. $120$
• C. $124$
• D. $116$

Answer 1

Answer: (B)

$120$

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 ${60}^o$

This is the least measure of an interior triangle of a regular polygon. $\therefore$ Here the exterior angle will be the greatest, since the interior and exterior angles are supplimentery to each other.

i.e The greatest exterior angle is ${180}^o-{60}^o={120}^o$

Hence, the answer is ${120}^o$.