Question

Let the formula relating the exterior angle and number of sides of a polygon be given as $\text{nA}={360}^{\circ }$.
The measure $\text{A}$ in degrees, of an exterior angle of a regular polygon, is related to the number of sides $\text{n}$, of the polygon by the above formula. If the measure of an exterior angle of a regular polygon is greater than ${50}^{\circ }$, what is the greatest number of sides it can have?

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

The correct option is C $7$

Sum of exterior angles for any polynomial is always ${360}^{\circ }$.

Since polynomial has $n$ angles, each with exterior angle is $A$, then
sum of exterior angles will be $nA$
Given, $nA=360$
$\therefore A=\frac{360}{n}$
We are given that: $A>50$

$\Rightarrow \frac{360}{n}>50$
$\Rightarrow 360>50n$
$\Rightarrow n<\frac{360}{50}$
$\Rightarrow n<7.2$
Hence, the greatest number of sides polygon can have is $7$.