2.8 What If It Is An Exterior Angle? Pg. 26 Exterior Angles of a Polygon.

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2.8 What If It Is An Exterior Angle? Pg. 26 Exterior Angles of a Polygon

2.8 – What If It Is An Exterior Angle?_____ Exterior Angles of a Polygon In the last section, you discovered how to determine the sum of the interior angles of a polygon with any number of sides. But what more can you learn about a polygon? Today you will focus on the interior and exterior angles of regular polygons.

2.42 – EXTERIOR ANGLES a. Examine the following pictures. With your team find the measure of each exterior angle shown. Then add the exterior angles up. What do you notice? x x x x x x

Sum exterior = ____________ 67° 98° 38° 71° 86° 360°

Sum exterior = ____________ 360° 90° 65° 30° 75° 45°55°

180(6 – 2) 6 = 108° Sum exterior = ____________ 360° 108° 72°

b. Compare your results from part (a). As a team, complete the conjectures below. The sum of the exterior angles of a polygon always adds to _____________. Each exterior angles of a regular polygon is found by _____________. 360° n

2.43 – MISSING ANGLES Find the missing angles of the regular polygons below. Be ready to justify your answers.

Central angle: ____________ Interior angle: ____________ Exterior angle: ___________ 360/4 = 90° 180(4-2) 4 90° 360/4 = 90° 90°

Central angle: ____________ Interior angle: ____________ Exterior angle: ___________ 360/6 = 60° 180(6-2) 6 120° 360/6 = 60° 60° 120° 60°

Central angle: ____________ Interior angle: ____________ Exterior angle: ___________ 360/9 = 40° 180(9-2) 9 140° 360/9 = 40° 40° 140° 40°

2.44 – USING INTERIOR AND EXTERIOR ANGLES Use your understanding of polygons to answer the questions below, if possible. If there is no solution, explain why not.

a. A regular polygon had exterior angles measuring 40°. How many sides did his polygon have? = 9 nonagon

b. If the measure of an exterior angle of a regular polygon is 15°, how many sides does it have? What is the measure of an interior angle? Show work = 24 sides 180(24-2) °

c. What is the measure of an interior angle of a regular 36-gon? Is there more than one way to find this answer? 180(36-2) ° = 10° Each interior angle = 180 – 10 = 170°

d. Suppose a regular polygon has an interior angle measuring 120°. Find the number of sides using two different strategies. Show all work. Which strategy was most efficient? 180(n – 2) n = 120° 180(n – 2) = 120n 180n – 360 = 120n –360 = –60n 6 = n 180(n – 2) n each interior angle =

d. Suppose a regular polygon has an interior angle measuring 120°. Find the number of sides using two different strategies. Show all work. Which strategy was most efficient? Each interior angle = 120° Each exterior angle = 60° = 6 sides

2.45 – CONCLUSIONS Complete the chart with the correct formulas needed to find the missing angles. How does the formula for the exterior angles compare to the formula for the central angles?

180(n – 2) n 360° n