Return to Mathematics IndexFinding the Sum of the Exterior and Interior Angles of a Polygon

David Drymiller Morgan Park High School

1744 W. Pryor Ave.

Chicago IL 60643

(312) 535-2550Objectives: To find the sum of the interior angles and the sum of the exterior angles of any polygon. To review linear measurement to the nearest sixteenth of an inch and angle measurement to the nearest degree. To construct a polygon and its exterior angles given the number of sides.Materials needed: For each group of four students the following is needed: a yardstick or meterstick, a large demonstration type protractor, chalk and instruction data record sheet. For each student the following is needed: ruler, protractor.Strategy: Each group draws a large 7, 8, 9, 10, 11 or 12 sided polygon on the floor or sidewalk with unequal sides. Measure each interior angle of the polygon to the nearest degree and record the results. Measure the length of each side and record the results. Find the sum of the interior angles of the polygon and record the answer. Extend each side of the polygon forming an exterior angle at each vertex. Measure each angle to the nearest degree and record the result. Find the sum of the exterior angles of the polygon and record the result. As a class, review the fact that the sum of the interior angles of a triangle is 180. Divide 4, 5, 6, 7, 8, 9, 10, 11, and 12 sided polygons into triangles showing the sum of the interior angles is 2x180, 3x180,..., 10x180, respectively. Generalize to the sum of the interior angles of a n sided polygon is (n-2)180. Draw a 7 sided polygon and its exterior angles and label the angles. Mark one end of the meterstick and place its center on the first vertex, slide the center along the side of the polygon to the next vertex, continue until arriving back at the starting vertex. The path of the marked end of the meter stick is a circle. Generalize to the sum of the exterior angles of a polygon is 360. Each student draws a 3, 4, 5, 6, 7, or 8 sided polygon and its exterior angles to the edge of the paper. Mark an arc on each exterior angle and cut each out. Place all of the vertices of the exteriors angles together forming a circle. Generalize to the sum of the exterior angles of a polygon is 360. Follow the above activity with an octagonal work sheet having the students record the measure of each angle and side on the figure. Place the sum of the interior angles in the center of the octagon. Tape the octagon onto a second sheet. Draw the exterior angles of the octagon on the second sheet and record each measure on the angle. Place the sum of the exterior angles on the bottom of the second sheet.