Name: Date: WORKSHEET : Polygons A polygon is a closed, planar shape connected by straight lines. Polygons can be categorized as regular or irregular. Polygons can be categorized as convex or concave. Polygons can be categorized as simple or complex. WORKSHEET : Polygons Interior/Exterior Angles ANSWERS : Polygons Interior/Exterior Angles KEY CONCEPTS: Definition of polygons and interior/exterior angle measures. 1. A polygon is a closed, planar shape connected by straight lines. a. Not closed ≠ polygon b. Not all straight lines ≠ polygon c. Planar means it is 2 dimensional; on an x-y coordinate plane for example d. Definitions of terms i. Vertex = The point where two lines meet on the polygon ii. Interior Angle = The angle inside the polygon between adjacent sides iii. Exterior Angle = If a line is extended from one side of the polygon past the vertex then the exterior angle is the angle between that line and the next adjacent side. 2. Names of polygons depend on the number of sides or interior angles (the same value). The smallest number of sides for a two dimensional polygon is 3. As n approaches infinity the polygon approaches a circle, but a circle is not a polygon due to its curves. Number of Sides, (n) Polygon Name 3 Triangle 4 Quadrilateral 5 Pentagon 6 Hexagon 7 Septagon(or Heptagon) 8 Octagon 10 Decagon 12 Dodecagon 15 Pentadecagon 100 Hecatgon 1,000 Chiliagon 1,000,000 Megagon 10100 Googolgon 3. The sum of interior angles of any n-sided polygon is... Sum Interior Angles = 180(n - 2) expressed in degrees e.g. Sum of Interior angles of a triangle (n=3) = 180(3 - 2) = 180 Sum of Interior angles of a quadrilateral (n=4) = 180(4 - 2) = 360 Sum of Interior angles of a pentagon (n=5) = 180(5 - 2) = 540 4. The sum of exterior angles always equals 360. The exterior angle sum does not change with the number of sides of the polygon. 5. The interior angle at any one vertex for a regular polygon is the same as the average interior angle of the polygon. e.g. The measure of any one interior angle of a "regular" pentagon is... Average = Sum/Count = 540/5 = 108 6. Interior Angle + Exterior Angles = 180 at any vertex. What are the implications of this at a concave vertex? .