To find the total of interior angles in any shape, use the formula (n – 2) × 180°, where n is the number of sides. For example, a quadrilateral has four sides, so the sum of its interior angles is (4 – 2) × 180° = 360°. This formula works for any closed figure with more than three sides.
For exterior angles, remember that the sum of all exterior angles in any shape is always 360°, regardless of the number of sides. To find an individual exterior angle, divide 360° by the number of sides. For a pentagon, for instance, each exterior angle will be 360° ÷ 5 = 72°.
Calculating Interior and Exterior Measurements
To calculate the sum of interior measurements, use the formula (n – 2) × 180°, where n represents the number of sides in the figure. For example, with a hexagon (6 sides), the sum is (6 – 2) × 180° = 720°. If you need to find the measurement of each individual interior segment, divide the total sum by the number of sides.
For exterior segments, the total of all such segments is always 360°. Divide this number by the number of sides to get the measurement of each exterior segment. For a heptagon (7 sides), divide 360° ÷ 7, which gives approximately 51.43° per exterior segment.
How to Calculate Interior Angles of Polygons
To find the sum of all interior measurements, apply the formula (n – 2) × 180°, where n is the number of sides. For example, for an octagon with 8 sides, the sum is (8 – 2) × 180° = 1080°.
To determine the measurement of each interior section, divide the total sum by the number of sides. For a hexagon (6 sides), each interior section is 720° ÷ 6 = 120°.
Steps to Find Exterior Angles in Polygons
To find the total of all exterior sections, use the constant value of 360° for any closed figure. The sum of all exterior sections is always 360°, no matter the number of sides.
To calculate the measurement of one exterior section, divide 360° by the number of sides in the shape. For a hexagon (6 sides), each exterior section will be 360° ÷ 6 = 60°.
