Polygon Angle Formulas and Practice
When working with polygons, remember these essential formulas. The sum of interior angles in any polygon is , where n is the number of sides. The sum of exterior angles always equals regardless of how many sides the polygon has.
For regular polygons (where all sides and angles are equal), each interior angle equals , and each exterior angle equals . You can find the number of sides by using (exterior angle) or by rearranging the interior angle formula.
Let's look at some practice problems. A pentagon (5 sides) has interior angles totaling , while a 27-gon has . For regular polygons, each interior angle in an octagon measures , and each exterior angle in a 20-gon equals .
Remember This! When a polygon has missing angles, subtract the known angles from the total sum to find the unknown angle. For example, when five angles of a hexagon are given, subtract their sum from .
