What is the formula for finding the exterior and the interior angles of a polygon?

The formulas for calculating the interior and exterior angles of a polygon are straightforward and useful in geometry.

Interior Angles

The formula to find the sum of the interior angles of a polygon is:

Sum of Interior Angles = (n - 2) × 180°

Here, n represents the number of sides in the polygon. To find the measure of each interior angle in a regular polygon (where all angles are equal), you can use:

Each Interior Angle = [(n - 2) × 180°] / n

Exterior Angles

For exterior angles, the sum of all exterior angles of any polygon is always:

Sum of Exterior Angles = 360°

To find the measure of each exterior angle in a regular polygon, you can use:

Each Exterior Angle = 360° / n

Example Calculation

• For a triangle (n = 3):
• Interior Angles: (3 - 2) × 180° = 180°
• Each Interior Angle: 180° / 3 = 60°
• Each Exterior Angle: 360° / 3 = 120°

These formulas help in understanding the properties of polygons and are essential for solving various geometric problems.