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Lesson 5.2

Investigation

Is there an exterior angle sum ?

Steps 1-5

Draw a large polygon and extend its sides to form a set of exterior angles. Measure all except one Use polygon sum to get the remaining angle measure use the linear pair conjecture to find it calculate the sum of the measure of the exterior angles repeat step 1-4 with other polygons

Exterior Angle Sum Conjecture

For any polygon, the sum of the measures of a set of exterior angles is 360° 

Steps 6-8

study the figure above using the polygon sum conjecture, write a formula for the measure of each interior angle in an equiangular polygon using the exterior angle sum conjecture, write the formula for the measure of each exterior angle in an equiangular polygon

Equiangular polygon Conjecture

You can find the measure of each interior angle of an equiangular n-gon by using either of these formulas: 180 - (360/n) or (180(n - 2)/n.