Section 8.1 Find Angle Measures in Polygons Definitions: 1. Polygon 2. Vertex 3. Convex 4. Non-convex ( )- 5. Equilateral 6. Equiangular 7. Regular 8. Diagonal - Identify each polygon by the number of sides, n. # of Sides Name 3 4 5 6 7 8 9 10 12 n n-gon Measure of exterior angle of regular polygon Measure of one interior angle of regular polygon Measure of all interior angles of regular polygon Determine if the figure is a polygon. If the figure is a polygon, classify it as convex or nonconvex. 1. 2. 3. 4. 5. 6. 7. 8. Use the diagram at the right to answer the following questions. 9. Name the polygon by the number of sides it has. B A C 10. Name all of the diagonals that have vertex E as an endpoint. G D 11. Name the consecutive angles to A. Draw a figure that fits the description. 12. A convex octagon 13. An equilateral quadrilateral that is not equiangular 14. An equiangular quadrilateral that is not equilateral F E 1. We can divide a polygon into triangles by drawing the diagonals from 1 vertex. Ex. Draw the diagonals from vertex A of pentagon ABCDE. How many s did you form?____ Draw the diagonals from vertex T in the hexagon PQRSTU. How many s did you form?____ Compare the # of sides in the polygon with the # of s formed. There are 2 fewer s than sides!! B A C E D P Q R U T S Therefore, the sum of all of the (interior) angles of a n-gon is (n - 2)180 LEARN! The sum of the angles of a pentagon is _______ 180 = __________ The sum of the angles of a hexagon is ________ 180 = __________ 2. Polygon Exterior Angles Theorem: The sum of the measures of the exterior angles of a convex polygon, only one exterior angle at each vertex, is 360. T Draw the following rays. GE , EO, OM , MT , TG What is the sum of these 5 exterior s?_______ If this pentagon is regular, then each of the 5 exterior angles would be _______. Show arithmetic. G M E O 3. (Theorem) The measure of each exterior angle of a regular polygon equals A Ex. 1 BCDEFG is a regular __________. ABG is an _____________ angle. mABG = ________. B 360 . n C G D F E Ex.2 What’s the measure of each exterior angle of a regular a.) decagon c.) nonagon b.) dodecagon d.) triangle Ex.3 If the exterior angle of a regular hexagon is 60, then the interior angle = _______. Explain: 4. To find the measure of each interior angle of a regular convex polygon, 360 , n = # of sides, then, subtract from 180. 1st find each exterior by n Ex. 1 Find the measure of each exterior angle and interior angle of a regular: a.) octagon b.) pentagon c.) 7-gon