Tutorial 6.5 Examples: Using Polygon Properties Example 1: Determine the sum of the angles in the polygon. There are 6 sides. Angle sum = 180(n – 2) Angle sum = 180(6 – 2) = 180(4) = 720
A
26
Example 2: Determine the missing angle and describe the polygon. There are 4 sides so the sum of the degrees is 180(4 –2) = 360 x = 360 – (26 + 30 + 68) x = 236, concave polygon
B
D
x
68 30
C
G
I 116
Example 3: Find the missing angle.
Sum of angles = 180(5 – 2) = 540 x = 540 – (114 + 121+ 116 + 96) x = 93
H 114
121
96
F
x E
Example 4: Find all missing angles. x = 180 – 74 x = 106 y = 180 – 107 y = 73
H
G
I
x
y
107 74
E
K
Example 5: Find y and z if x = 114.
1. Find y using supplementary angles property. 2. Find z using polygon angles sum. y = 180 – 122 y = 58 z = 360 – (58 + 114 + 53) z = 135
122 y
M N
x
J
z
53
L