Each exterior angle of a regular polygon is approximately 21.18 degrees. What is the sum of the interior angles of a polygon?
2 Answers
Sum of interior angles
Explanation:
If each exterior angle is
then each interior angle is
For a regular polygon with
the sum of the interior angles is
but since each of the
the sum of the interior angles is also
So we have
which simplifies to
or
So the sum of the interior angles is
The sum of the angles in a 17-sided polygon is 2700°
Explanation:
Sum of exterior angles in a polygon is always 360 degrees.
To find the number of side of polygons, we must divide 360 degrees by the size of the exterior angle
By using this property,
Number sides of polygon=
Number of sides of the polygon =
However, the number of sides must be a whole number.
There are 17 sides
After we get the number of sides of a polygon, we can find the total of the interior angle by using
Total of interior angles is