Download Classifying Polygons: Section 9

Section 3.3 Angles of Polygons
POD: Find the exterior angle of the triangle.
1.)
x = 128°
2.)
Exterior Angle = 108° (a = 54)
Objective: Students will be able to find the measures of interior and exterior angles of polygons.
Vocabulary:
Polygon: A closed plane figure made up of three or more line segments that only intersect at their
endpoints.
Convex: When every line segment connecting any
two vertices lies entirely inside the polygon.
Concave: When at least one line segment
connecting any two vertices lies outside the
polygon.
Sum of Interior Angles: d = 180(n – 2)
where d = degrees and n = number of sides
1.)
If a figure has 10 sides, what is the sum of the interior angles?
s = 180(10-2)
s = 180(8)
s = 1,440°
2.)
If a figure has 14 sides, what is the sum of the interior angles?
s = 180(14-2)
s = 180(12)
s = 2,160°
3.)
Find the value of x.
First count the number of sides!
s = 180(7 – 2)
s = 180(5)
s = 900°
x + 128 + 130 + 120 + 115 + 145 + 140 = 900
x + 778 = 900
-778 -778
x = 122°
Sum of Exterior Angles:
Find the value of x and  1.
4.)
z + 124 + z + 26 = 360
2z + 150 = 360
-150 -150
2z = 210
2
2
z = 105°
 1 = 105 + 26 = 131°
360°
5.)
z + 45 + z + 74 + 78 + 55 = 360
1
2z + 252 = 360
-252 -252
2z = 108
2
2
z = 54°
 1 = 54 + 45 = 99°
1