Sec 11-1 Angle Measures in Polygons

1. Sec 11-1Angle Measures in Polygons

2. Polygon - A closed coplanar figure formed by three or more segments, called sides • A Polygon has to meet the following conditions: • It is formed by three or more segments, called sides. • No two sides with a common endpoint are collinear. • Each side intersects exactly two other sides, one at each endpoint. • Each endpoint of a side is a vertex of the polygon.

3. 3 sides 4 sides 5 sides 6 sides 7 sides 8 sides 9 sides 10 sides 12 sides 15 sides n sides Types of Polygons Triangle Octagon Quadrilateral Nonagon Pentagon Decagon Hexagon Dodecagon Heptagon Pentadecagon n - gon a polygon where all the sides are congruent Equilateral Polygon – Equiangular Polygon – Regular Polygon – a polygon where all the angles are congruent a polygon that is both equilateral and equiangular

4. Convex Polygon – A polygon whose sides are not contained in lines that go into the interior of the polygon Concave Polygon – A polygon that has at least one side that is contained in a line that goes into the interior of the polygon

5. Formula for Sum of Interior Angles(Polygon Angle-Sum Theorem) n represents the number of sides in polygon Ex#1 Find the sum of the interior angles of a heptagon = 5(180o) = 900o

6. The Exterior Angle-Sum Theorem The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360o 1 5 2 4 3

7. Ex #2: What is the measure of each interior angle in a regular octagon? Ex #3: If the measure of an exterior angle of a regular polygon is 30o, what is the measure of each interior angle, and what type of polygon is it? The polygon is a dodecagon