Find the sum of the measures of the interior angles and the sum of exterior angles of a seventeen sided convex polygon

interior-angles
convex-polygon

#1

find the sum of the measures of the interior angles and the sum of exterior angles of a seventeen sided convex polygon

Answer:

The sum of interior angles can be calculated by using the formula:
(n−2)∗180\textdegree
where “n” is equal to the number of sides.

Therefore the sum of the interior angles is 2700\textdegree. Exterior angles are 360\textdegree minus interior angles.

While we don’t know the exact dimensions of the polygon, we know it’s convex, so we simply work in averages.

We find out the value of the average interior angle my doing 2700/17 which is roughly 158.82\textdegree.

360−158.82=201.18 for the external angle, then multiply 201.18 by the number of sides, which is 17.
201.18∗17=3420.06

et voila.