Section 3 5 Angles of a Polygon Polygon

Section 3 -5 Angles of a Polygon

Polygon • Means: “many-angled” • A polygon is a closed figure formed by a finite number of coplanar segments a. Each side intersects exactly two other sides, one at each endpoint. b. No two segments with a common endpoint are collinear

Examples of polygons:

Two Types of Polygons: 1. Convex: If a line was extended from the sides of a polygon, it will NOT go through the interior of the polygon.

2. Nonconvex: If a line was extended from the sides of a polygon, it WILL go through the interior of the polygon.

Polygons are classified according to the number of sides they have. *Must have at least 3 sides to form a polygon. Special names for Polygons *n stands for number of sides. Number of Sides Name 3 Triangle 4 5 6 7 8 9 10 n Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon n-gon

Diagonal • A segment joining two nonconsecutive vertices *The diagonals are indicated with dashed lines.

Definition of Regular Polygon: • a convex polygon with all sides congruent and all angles congruent.

Interior Angle Sum Theorem • The sum of the measures of the interior angles of a convex polygon with n sides is

One can find the measure of each interior angle of a regular polygon: 1. Find the Sum of the interior angles 2. Divide the sum by the number of sides the regular polygon has.

One can find the number of sides a polygon has if given the measure of an interior angle

Exterior Angle Sum Theorem • The sum of the measures of the exterior angles of any convex polygon, one angle at each vertex, is 360.

One can find the measure of each exterior angle of a regular polygon: One can find the number of sides a polygon has if given the measure of an exterior angle