13 3 Angles and Polygons Polygons Sides Name

13. 3 Angles and Polygons

Polygons Sides Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon 11 Undecagon 12 Dodecagon

Regular Polygon All of the sides are equal and all of the angles are equal

Interior Angles Angle on the inside of a polygon The sum of the interior angles of a polygon with n sides is found by (n-2) • 180°

Sum of Interior Angles of a 3 sided figure (n - 2) · 180° Angles of a 5 sided figure (n - 2) · 180° (3 - 2) · 180° (1) · 180° (5 - 2) · 180° (3) · 180° 540°

Interior Angles of a Regular Polygon Since all of the angles in the regular polygon are equal, each angle is equal to (n-2) • 180° n

Find the measure of one interior angle in a regular hexagon. (n-2) • 180° n (6 -2) • 180° 6 (4) • 180° 6 720° 6 120°

Find the measure of one interior angle in a regular decagon (n-2) • 180° n (10 -2) • 180° 10 (8) • 180° 10 144°

Exterior Angles Angle next to an interior angle of a polygon formed by extending the side. ***Exterior and Interior angles are supplementary!!!***

Sum of Exterior Angles The sum of the exterior angles of ANY polygon is equal to 360° x° 124° x° x + 124 + x + 124 = 360° 2 x + 248 = 360° 2 x = 112° x = 56°

Exterior Angles of a Regular Polygon All of the angles in the regular polygon are equal, each angle is equal to 360° n Find the measure of each exterior angle of a regular pentagon. 360° n 360° 5 72°

Find the measure of one exterior angle and one interior angle of a regular 20 -gon Interior Exterior (n-2) • 180° n 360° n (20 -2) • 180° 20 360° 20 (18) • 180° 20 18° 162° Check: 162° + 18° = 180°