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Edgar's Question from Facebook: Convex Polygon

Sudharaka

Well-known member
MHB Math Helper
Feb 5, 2012
1,621
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

Administrator
Staff member
Feb 24, 2012
13,775
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.