1. 1 Objectives Define polygon, concave / convex polygon, and regular polygon Find the sum of the measures of interior angles of a polygon Find the sum of the measures of exterior angles of a polygon

2. 2 Definition of polygon A polygon is a closed plane figure formed by 3 or more sides that are line segments; –the segments only intersect at endpoints –no adjacent sides are collinear Polygons are named using letters of consecutive vertices

3. 3 Concave and Convex Polygons A convex polygon has no diagonal with points outside the polygon A concave polygon has at least one diagonal with points outside the polygon

4. 4 Regular Polygon Definition An equilateral polygon has all sides congruent An equiangular polygon has all angles congruent A regular polygon is both equilateral and equiangular Note: A regular polygon is always convex

5. 5 Sum of Interior Angles in Polygons Convex Polygon# of Sides # of Triangles from 1 Vertex Sum of Interior Angle Measures Triangle311* 180 = 180 Quadrilateral422* 180 = 360 Pentagon533* 180 = 540 Hexagon644* 180 = 720 Heptagon755* 180 = 900 Octagon866* 180 = 1080 n-gonnn – 2(n – 2) * 180

6. 6 Example: Sum of Interior Angles Find m ∠ X Solution: The sum of the measures of the interior angles for a quadrilateral is (4 – 2) * 180 = 360 The marks in the illustration indicate that m ∠X = m∠Y. So the sum of all four interior angles is m∠X + m∠X + 100 + 90 = 360 2 m∠X + 190 = 360 2 m∠X = 170 m∠X = 85