5.2 exterior angles of a polygon objective: discover the sum of the measures of the exterior angles...

5.2 Exterior Angles of a PolygonObjective:•Discover the sum of the measures of the exterior angles of a polygon.•Practice construction skills.•Develop reasoning, problem-solving skills, and cooperative behavior.

• Step 1: Using the same shape from 5.1, re-draw your polygon, extending the sides to form a set of exterior angles

• Step 2: measure all the interior angles of the polygon, except one, Calculate the remaining interior angle using the Polygon Sum Conjecture. Check the answer with your protractor

Conjecture Protractor

• Step 3: Use the linear pair conjecture to calculate the measure of each exterior angle.

• Step 4: Calculate the sum of the measures of the exterior angles. Share your results.

Exterior Angle Sum ConjectureFor any polygon, the sum of the measures of a set of exterior angles is _______________

Equiangular Polygon Conjecture You can find the measure of each interior angle of an equiangular n-gon by using either of these formulas: _____________________ or ______________________

360

180-360/n (180(n-2))/n