Math I Unit 3 Worksheet Name ____________________ Pd.____
Find the value of x and the missing angle measures
1) 2)
5x° 60°
x°
3x°
x° x°
5x + x + 3x = 180; x = 20
angle measures: 20°, 60°, 100° 60 + 2x = 180; x = 60
angle measures: 60°, 60°, 60°
3) (x + 10)° 4)
(2x – 165)°
(x – 15)°
(2x + 10)° x°
4x + 20 = 180; x = 40 90 + 2x – 165 + x – 15 = 180; x = 90
angle measures: 40°, 50°, 90° angle measures: 15°, 75°, 90°
Find the sum of the measures of the interior angles of the convex polygon: (n – 2)180
5) 10-gon 6) 12-gon 7) 15-gon 8) 18-gon
1, 440° 1,800° 2,340° 2,880°
9) 20-gon 10) 30-gon 11) 40-gon 12) 100-gon
3,240° 5,040° 6,840° 17,640°
Find the value of x
13) 14) 15)
x + 424 = 540; x = 116 x + 443 = 540; x = 97 x + 783 = 900; x = 117
16) 17) 18)
x + 236 = 360; x = 124 x + 574 = 720; x = 146 x + 420 = 540; x = 120
19) 20) 21)
(6-2)(180)/6; x = 120 (8-2)(180)/8; x = 135 (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° 25) 120° 26) 140°
144 = (n-2)180/n n = 6 (hexagon) n = 9 (nonagon)
144n = 180n - 360
-36n = -360
n = 10 (decagon)
27) 108° 28) 156° 29) 157.5°
n = 5 (pentagon) n = 15 (15-gon) n = 16 (16-gon)
You are given the number of sides of a regular polygon. Find the measure of each exterior
angle.
30) 12 31) 11 32) 21 33) 15
360/12; 30° 360/11; 32 ° ≈32.72° 360/21; 17 ° ≈ 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° 35) 90° 36) 45° 37) 30°
60 = 360/n n = 4 (quadrilateral) n = 8 (octagon) n = 12 (dodecagon)
60n = 360;
n = 6 (hexagon)
38) 20° 39) 72° 40) 10° 41) 15°
n = 18 (18-gon) n = 5 (pentagon) n = 36 (36-gon) 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)°
D) 65 (2x – 15)°
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 x
125°
A) 55°, 125° C) 55°, 90°
B) 90°, 90° D) 90°, 125°
55° y
** You will have to show students Linear Pair Postulate to find y first.***
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°
B C
B) 1080° 4x° 3x°
C) 1260°
48) What is the measure of angle B? D x° 2x
A D
°
A) 36° C) 108°
B) 90° D) 144°
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°
140°
B) 120°
C) 45°
D) 40°
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° 60) 540° 61) 900°
180 = (n-2)180 n = 5 (pentagon) n = 7 (heptagon)
180 = 180n – 360
n = 3 (triangle)
62) 1800° 63) 2520° 64) 3960°
n = 12 (dodecagon) n = 16 (16-gon) n = 24 (24-gon)
65) 5040° 66) 5940° 67) 8640°
n = 30 (30-gon) n = 35 (35-gon) 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) 70) 71)
x = 720 – 574; x = 146 x = 540 – 420; x = 120 x = 360 – 278; x = 82
72) 73) 74)
90 60
° °
4x
2x
°
° x°
25x – 15 = 360; x = 15 7x + 150 = 360; x = 30 x + 141 = 180; x = 39
75) 76) 77)
x = (8-2)(180)/8; x = 135 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 175.2 = (n-2)(180)/n
140n = 180n – 360 175.2n = 180n - 360
-40n = -360 -4.8n = -360
n=9 n = 75
nonagon 75-gon
86) Each exterior angle of the regular n-gon 87) Each exterior angle of the regular n-gon
has a measure of 45°. has a measure of 3°.
n = 8 (octagon) n = 120 (120-gon)