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Geometry 5.1 Activity – Interior and Exterior Angles Name ____________________________ Pd _____ Sum of the Interior Angles in Polygons Draw all of the diagonals from the marked vertex until the polygon is separated into non-overlapping triangles. Complete the table for each polygon below. Based on the patterns observed in the first five polygons, generalize what the angle sum for an n-gon would be. Quadrilateral Pentagon Heptagon Polygon Hexagon Octagon Number of sides Number of angles Number of triangles Total degrees in a triangle Total degrees in the polygon ********* ********* ********* ********* ********* Quadrilateral Pentagon Hexagon Heptagon Octagon ********* n-gon Describe the pattern you see using the pattern with n representing the number of sides. Sum of the Exterior Angles in Polygons Quadrilateral: # of sides = __________ Pentagon: # of sides = __________ Sum of the Exterior Angles = __________ Sum of the Exterior Angles = __________ Hexagon: # of sides = __________ Heptagon: # of sides = __________ Sum of the Exterior Angles = __________ Sum of the Exterior Angles = __________ Octagon: # of sides = __________ Nonagon: # of sides = __________ Sum of the Exterior Angles = __________ Sum of the Exterior Angles = __________ Conclusion: The sum of the exterior angles in any polygon is ____________.
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