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Geometry
Polygons Worksheet
Name: ____________________________
Period: ____
Name each regular polygon. Find the measure the indicated angles.
1. Name: ___________________ 2. Name: ___________________
Sum of Interior ’s: _____
One Interior : _____
Sum of Exterior ’s: ______
One Exterior : ______
4. Name: ___________________
Sum of Interior ’s: _____
One Interior : _____
Sum of Exterior ’s: ______
One Exterior : ______
3. Name: ___________________
Sum of Interior ’s: _____
One Interior : _____
Sum of Exterior ’s: ______
One Exterior : ______
5. Nonagon
6. Dodecagon
Sum of Interior ’s: _____
One Interior : _____
Sum of Exterior ’s: ______
One Exterior : ______
Sum of Interior ’s: _____
One Interior : _____
Sum of Exterior ’s: ______
One Exterior : ______
7. If the sum of the interior angles
of a regular polygon is 900°,
find the number of sides.
8. If the measure of one interior
angle of a regular polygon is
144°, find the number of sides.
9. If the measure of one interior
angle of a regular polygon is
160°, find the number of sides.
Find the value of each variable.
10.
11.
12.
Sum of Interior ’s: _____
One Interior : _____
Sum of Exterior ’s: ______
One Exterior : ______
y°
117°
120°
x°
105°
85°
53°
116°
100°
115°
129°
120°
130°
x°
135°
125°
13.
14.
15.
3x°
w°
x°
4x°
2x°
(w – 13)° y°
z°
x°
(w + 10)°
16.
110°
17.
y°
18.
100°
87°
z°
Find m1 and then the m2. Justify each answer. On 18, find m1, then the m2, and then m3.
19.
20.
21.
80°
112°
1
1
1
2
2
2
75°
3
m1 = _____ because __________
m1 = _____ because __________
m1 = _____ because __________
_____________________ _____________________
m2 = _____ because __________
m2 = _____ because __________
_____________________ _____________________
_____________________
m2 = _____ because ________
_____________________
m3 = _____ because ________
_____________________
Based on the markings which lines or segments must be parallel? Justify your answer.
22.
23.
24.
T
Y
p
D
A
n
B
l
m
W
X
Z
C
25. Find x, and determine if n is parallel to m. Justify.
26. Find x, and determine if AD is parallel to BC.
E
Justify.
x°
(2x – 9)°
(3x)°
(3x + 8)°
139°
m
A
1
(2x + 4)°
D
n
(9x + 7)°
79°
B
C
Write and solve a system of equations to find the value of each variable.
27.
(10y – 6)
(7x)
(3x)
(6x +6) (4x +2y)
28. Note: You can’t use the Triangle Exterior Angle Theorem with the given information. You should use the
Vertical Angle Theorem and the Triangle Sum Theorem.
(8x + 1)
(7y)
(10x)
(15y + 5)