One exterior angle of a regular polygon measures 36. What is the sum of the polygon's interior angle measures?
In the diagram above, let your exterior angle be
The angle sum of any polygon is given by
Therefore, the angle sum of the polygon is equal to the one interior angle multiplied by the number of angles there are. Now since the number of angles is equivalent to the number of sides, we can write it like this:
Since the polygon has 10 sides, then it must be a decagon.
Sum of polygon's interior angles is
Let the number of sides of regular polygon be
Exterior angle of regular polygon is
equal sides. Sum of polygon's interior angles is