The formula for finding the sum of the interior angles of a polygon is given by the equation:
Sum of Interior Angles = (n – 2) × 180°
Here, n represents the number of sides of the polygon. For example, in a triangle (which has 3 sides), the sum of the interior angles would be (3 – 2) × 180° = 180°. In a quadrilateral (4 sides), it would be (4 – 2) × 180° = 360°.
As for the exterior angles, the formula is much simpler. The sum of the exterior angles of any polygon is always:
Sum of Exterior Angles = 360°
This holds true regardless of the number of sides in the polygon. Each exterior angle can be calculated as:
Exterior Angle = 180° – Interior Angle
In summary, while the sum of the interior angles changes depending on the number of sides, the sum of the exterior angles remains constant at 360°. Understanding these formulas helps in solving various geometric problems related to polygons.