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 D
the degrees is 180(4 –2) = 360 x
x = 360 – (26 + 30 + 68)
x = 236, concave polygon 68
B 30
C
G I
121 116
Example 3:
Find the missing angle.
Sum of angles = 180(5 – 2) H 114
96
= 540 F
x = 540 – (114 + 121+ 116 + 96)
x = 93
x
E
Example 4: G I
Find all missing angles. x y
x = 180 – 74
x = 106
y = 180 – 107
y = 73
107
H
74
E
K
x
Example 5:
Find y and z if x = 114. J
z
1. Find y using supplementary angles
property.
53
2. Find z using polygon angles sum. L
122 y
y = 180 – 122 M
y = 58 N
z = 360 – (58 + 114 + 53)
z = 135