What are the formula for finding exterior and interior angles of a polygon?
Answer: Interior Angles of a Regular Polygon with n sides: Interior angle = (180n - 360)/n
Exterior Angles of a Regular Polygon with n sides: Exterior angle = 360°/n
We will use the formula of the sum of interior angles and exterior angles to answer this question.
The sum of interior angles is given by 180 (n - 2), where n is the number of sides.
Since all interior angles in a regular polygon are equal, we can say that the interior angle of polygon = sum of interior angles ÷ number of sides
= 180 (n - 2) ÷ n
= (180n - 360)/n
Now, we know that sum of exterior angles of a regular polygon is 360°
The formula to calculate the measure of an exterior angle is: exterior angle of polygon = 360° ÷ number of sides = 360°/n