Edgar's Question from Facebook: Convex Polygon

[Sudharaka]

Edgar from Facebook writes:

The sum of the measures of the interior angles of a convex polygon is ten times the sum of the measures of its exterior angles. Find the number of sides of a polygon.

Hello could you please help me to solve this problem?

 

[MarkFL]

Hello Edgar,

We need two theorems here:

• For a convex polygon having $n$ sides, the sum $S$ of the interior angles is given by $S=(n-2)180^{\circ}$.
• Regardless of the number of sides, the sum of the exterior angles is $360^{\circ}$.

Hence, we need to solve the following for $n$:

$(n-2)180^{\circ}=10\cdot360^{\circ}$

Divide through by $180^{\circ}$:

$(n-2)=10\cdot2$

$n-2=20$

$n=22$

Thus, we have found a convex polygon having 22 sides meets the stated requirement.