Math I
Unit 3 Worksheet
Name ____________________ Pd.____
Find the value of x and the missing angle measures
1)
x°
2)
5x°
60°
3x°
x°
5x + x + 3x = 180; x = 20
angle measures: 20°, 60°, 100°
3)
x°
60 + 2x = 180; x = 60
angle measures: 60°, 60°, 60°
4)
(x + 10)°
(2x – 165)°
(x – 15)°
x°
(2x + 10)°
90 + 2x – 165 + x – 15 = 180; x = 90
angle measures: 15°, 75°, 90°
4x + 20 = 180; x = 40
angle measures: 40°, 50°, 90°
Find the sum of the measures of the interior angles of the convex polygon: (n – 2)180
5) 10-gon
1, 440°
6) 12-gon
1,800°
7) 15-gon
2,340°
8) 18-gon
2,880°
9) 20-gon
3,240°
10) 30-gon
5,040°
11) 40-gon
6,840°
12) 100-gon
17,640°
Find the value of x
13)
x + 424 = 540; x = 116
14)
x + 443 = 540; x = 97
15)
x + 783 = 900; x = 117
16)
17)
x + 236 = 360; x = 124
19)
x + 574 = 720; x = 146
20)
(6-2)(180)/6; x = 120
(8-2)(180)/8; x = 135
18)
x + 420 = 540; x = 120
21)
(5-2)(180)/5; x = 108
22)
A convex quadrilateral has interior angles that measure 80°, 110°, and 80°. What is the
measure of the fourth interior angle?
x + 80 + 110 + 80 = 360; x = 90; The fourth interior angle is 90°.
23)
A convex pentagon has interior angles that measure 60°, 80°, 120°, and 140°. What is the
measure of the fifth interior angle?
60 + 80 + 120+ 140 + x = 540; x = 140; The fifth interior angle is 140°.
You are given the measure of each interior angle of a regular n-gon. Find the value of n.
***Show students how to set up the equation and cross multiply. Emphasize that n is the
number of sides of the polygon.****
24) 144°
144 = (n-2)180/n
144n = 180n - 360
-36n = -360
n = 10 (decagon)
27) 108°
n = 5 (pentagon)
25) 120°
n = 6 (hexagon)
26) 140°
n = 9 (nonagon)
28) 156°
n = 15 (15-gon)
29) 157.5°
n = 16 (16-gon)
You are given the number of sides of a regular polygon. Find the measure of each exterior
angle.
30) 12
360/12; 30°
31) 11
𝟖
360/11; 32𝟏𝟏° ≈32.72°
32) 21
33) 15
𝟏
360/21; 17𝟕° ≈ 17.14°
360/15; 24°
You are given the measure of each exterior angle of a regular n-gon. Find the values of n.
34) 60°
60 = 360/n
60n = 360;
n = 6 (hexagon)
38) 20°
n = 18 (18-gon)
35) 90°
n = 4 (quadrilateral)
39) 72°
n = 5 (pentagon)
36) 45°
n = 8 (octagon)
37) 30°
n = 12 (dodecagon)
40) 10°
n = 36 (36-gon)
41) 15°
n = 24 (24-gon)
Multiple Choice Questions (Show some work)
42) What is the sum of the exterior angle measures in an irregular pentagon? B
A) 180°
C) 540°
B) 360°
D) 900°
43) What is the value of x in the diagram below? D
(x + 15)°
x°
A) 99
B) 75
C) 72
(x + 35)°
(2x – 15)°
D) 65
44) What is the measure of each interior angle of a regular octagon? C
A) 360°
C) 135°
B) 180°
D) 120°
45) Find the values of x and y in the figure. A
A) 55°, 125°
C) 55°, 90°
B) 90°, 90°
D) 90°, 125°
** You will have to show students Linear Pair Postulate to find y first.***
x
125°
55° y
46) If a regular octagon has eight sides, what is the measure of each exterior angle? C
A) 15°
C) 45°
B) 30°
D) 360°
47) What is the sum of the interior angles of an octagon? B
A) 1440°
D) 360°
C
B
B) 1080°
4x°
3x°
C) 1260°
48) What is the measure of angle B? D
A) 36°
C) 108°
B) 90°
D) 144°
A
x°
2x
°
49) What is the measure of an exterior angle if the regular polygon has 18 sides? B
A) 18°
B) 20°
C) 22°
D) 24°
50) What is the sum of the measures of the interior angles in the hexagon? C
A) 180°
2
B) 360°
C) 720°
D) 900°
135°
51) What is the measure of 1 ? A
45°
125°
1
A) 135°
B) 120°
C) 45°
D) 40°
140°
D
52) What is the measure of 2 ? B
A) 90°
B) 95°
C) 185°
D) 320°
Find the sum of the measures of the interior angles of the indicated convex polygon.
(n - 2)180
53) Hexagon
54) Dodecagon
55) 11-gon
720°
1,800°
1,620°
56) 15-gon
57) 20-gon
58) 40-gon
2,340°
3,240°
6,840°
The sum of the measures of the interior angles of a convex polygon is given. Classify
the polygon by the number of sides.
59) 180°
180 = (n-2)180
180 = 180n – 360
n = 3 (triangle)
62) 1800°
n = 12 (dodecagon)
60) 540°
n = 5 (pentagon)
61) 900°
n = 7 (heptagon)
63) 2520°
n = 16 (16-gon)
64) 3960°
n = 24 (24-gon)
65) 5040°
n = 30 (30-gon)
66) 5940°
n = 35 (35-gon)
67) 8640°
n = 50 (50-gon)
68) The measures of the interior angles of a convex octagon are 45x°, 40x°, 155°, 120°, 155°,
38x°, 158°, and 41x°. What is the measure of the smallest interior angle
45x + 40x + 155 + 120 + 155 + 38x + 158 + 141x = 1080; x = 3
The smallest angle measure is 38x = 114°.
Find the value of x
69)
x = 720 – 574; x = 146
70)
x = 540 – 420; x = 120
71)
x = 360 – 278; x = 82
72)
73)
74)
90
°
60
°
4x
°
2x
° x°
25x – 15 = 360; x = 15
75)
7x + 150 = 360; x = 30
76)
x = (8-2)(180)/8; x = 135
x + 141 = 180; x = 39
77)
x = (6-2)(180)/6; x = 120
x = (5-2)(180)/5; x = 108
Find the measures of an interior angle and an exterior angle of the indicated polygon.
**You can show students to use two different formulas for this, or they can find one and use
linear pair postulate to find the other one.**
78) Regular Triangle
79) Regular octagon
80) Regular 16-go
60°; 120°
135°; 45°
157.5°; 22.5°
81) Regular 45-gon
82) Regular 60-gon
83) Regular 100-gon
172°; 8°
174°; 6°
176.4°; 3.6°
Find the value of n for each regular n-gon described.
84) Each interior angle of the regular n-gon
85) Each interior angle of the regular n-gon
has a measure of 140°.
has a measure of 175.2°.
140 = (n-2)(180)/n
140n = 180n – 360
-40n = -360
n=9
nonagon
86) Each exterior angle of the regular n-gon
has a measure of 45°.
n = 8 (octagon)
175.2 = (n-2)(180)/n
175.2n = 180n - 360
-4.8n = -360
n = 75
75-gon
87) Each exterior angle of the regular n-gon
has a measure of 3°.
n = 120 (120-gon)