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: 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 Number of Sides Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Heptagon 8 Octagon 9 Nonagon 10 Decagon n n-gon *n stands for number of sides.

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: Find the Sum of the interior angles 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