2.7

What If It Is An Exterior Angle?

Pg. 25

Exterior Angles of a Polygon

2.7 – 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.

2.34 – EXTERIOR ANGLESa. 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

= 120°

Sum exterior = ____________ 360°

120°60°

60°

60°60°

60°

60°

http://www.cpm.org/flash/technology/externalangles.swf

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°

360°n

2.35 – MISSING ANGLESFind the value of x.

x + 86 + 59 + 96 + 67 = 360

x + 308 = 360

x = 52°

2x + 59 + 54 + x + 80 + 59 = 360

3x + 252 = 360

x = 36°

3x = 108

2.36 – USING INTERIOR AND EXTERIOR ANGLESUse 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?

36040

= 9

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.

36015

= 24 sides180(24-2)

24

165°

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)36

170°

36036

= 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) = 120n180n – 360 = 120n

–360 = –60n6 = n

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°

36060

= 6 sides

2.45 – CONCLUSIONSComplete 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)

180(n – 2) n

360°

360° n