Angles in Polygons

Interior and Exterior Angles This is a regular pentagon. By extending each side we can see the exterior angles

Interior and Exterior Angles All the exterior angles can fit around a point, as follows: This means that the exterior angles on a polygon add up to 360°

Interior and Exterior Angles The interior angles on a polygon are on the inside! interior and exterior angles Notice that the make a straight line That means: int + ext = 180°

Calculate the exterior angle and interior angle on a regular octagon. Example: Calculate the exterior angle and interior angle on a regular octagon. sum of exterior angles = 360° 360 8 exterior angle = = 45° int + ext = 180° int + 45 = 180° int = 135°

Investigating the sum of interior angles on any polygon

Name of polygon Number of sides Number of triangles Sum of interior angles Triangle 3 1 1 × 180 = 180° Quadrilateral 4 2 2 × 180 = 360° Pentagon 5 3 × 180 = 540° Hexagon 6 4 × 180 = 720° Heptagon 7 5 × 180 = 900° Octagon 8 6 × 180 = 1080°

Interior and Exterior Angles The sum of interior angles in any polygon is calculated by... Sum int = (n-2) × 180 where n is the number of sides on the polygon

Find the sum of interior angles on a dodecagon. Example: Find the sum of interior angles on a dodecagon. A dodecagon = 12 sides Sum int = (n - 2) × 180 Sum int = (12 - 2) × 180 = 1800°

Example: Sum of int = (n – 2) × 180 = (5 – 2) × 180 = 3 × 180 = 540° 75° 140° 2x 3x 3x + 5 75° 140° 2x Sum of int = (n – 2) × 180 = (5 – 2) × 180 = 3 × 180 = 540° 2x + 3x + 5 + 3x + 75 + 140 = 540° 8x + 220 = 540° 8x = 320° x = 40°