Polygon Angle Sums (Set 2) Worksheet

Sample problems

Use the interior angle sum $(n-2)\cdot 180^{\circ }$ and the fact that the exterior angles of any convex polygon total $360^{\circ }$. For a regular $n$-gon, each interior angle is $\frac{(n-2)\cdot 180^{\circ }}{n}$ and each exterior angle is $\frac{360^{\circ }}{n}$. Show your work.

1. 1. Find the sum of the interior angles of a quadrilateral ($n=4$).
2. 2. Find the sum of the interior angles of a heptagon ($n=7$).
3. 3. Find the sum of the interior angles of a polygon with $15$ sides.
4. 4. Which expression gives the measure of each exterior angle of a regular polygon with $n$ sides?
   • $(n-2)\cdot 180^{\circ }$
   • $\frac{(n-2)\cdot 180^{\circ }}{n}$
   • $\frac{360^{\circ }}{n}$
   • $180^{\circ }-n$

Plus 10 more problems and a full answer key in the PDF.