Kuta Software - Infinite Algebra
Name___________________________________
Angles and Angle Measure
Date________________ Period____
Convert each degree measure into radians and each radian measure into degrees.
1) 325°
3) 
2) 60°


4)


6) °
5) 570°
Convert each decimal degree measure into degrees-minutes-seconds and each
degrees-minutes-seconds into decimal degrees.
7) °
8) ° ' "
9) ° ' "
10) °
Find the measure of each angle.
11)
12)
y
y


x
x
°
13)
14)
y
y
°
x
x


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Worksheet by Kuta Software LLC
15)
16)
y
y
°


x
x
Draw an angle with the given measure in standard position.
17) °
18) °
y
y
x
19) °
x
20)
y


y
x
x
21) 


22) °
y
y
x
x
State the quadrant in which the terminal side of each angle lies.
23) °
24) 


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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra
Name___________________________________
Angles and Angle Measure
Date________________ Period____
Convert each degree measure into radians and each radian measure into degrees.


1) 325°
2) 60°




-240°

5) 570°

3) 
4)


345°
6) ° 


Convert each decimal degree measure into degrees-minutes-seconds and each
degrees-minutes-seconds into decimal degrees.
7) °
8) ° ' "
° ' "
°
9) ° ' "
10) °
°
–° ' "
Find the measure of each angle.
11)
12)
y


y


x
x
°
°
13)
14)
y

y


°
x
x


°
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Worksheet by Kuta Software LLC
15)


y
16)
°
y
°


x
x
Draw an angle with the given measure in standard position.
17) °
18) °
y
y
x
19) °
x
20)
y


y
x
x
21) 


22) °
y
y
x
x
State the quadrant in which the terminal side of each angle lies.
23) ° III
24) 

III

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Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra
Name___________________________________
Arc Length and Sector Area
Date________________ Period____
Find the length of each arc. Round your answers to the nearest tenth.
1)
2)
11 ft
270°
13 ft
315°
3)
4)
π
6 13 in
16 ft
3π
2
5) r = 18 cm, θ = 60°
7) r = 9 ft, θ =
7π
4
6) r = 16 m, θ = 75°
8) r = 14 ft, θ =
19π
12
Find the length of each arc. Do not round.
9)
10)
315°
150°
19 ft
3π
4
13 ft
8 cm
11)
12)
π
2
14 cm
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-1-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra
Name___________________________________
Arc Length and Sector Area
Date________________ Period____
Find the length of each arc. Round your answers to the nearest tenth.
2)
1)
11 ft
270°
13 ft
315°
60.5 ft
61.3 ft
3)
4)
π
6 13 in
16 ft
3π
2
75.4 ft
6.8 in
5) r = 18 cm, θ = 60°
6) r = 16 m, θ = 75°
18.8 cm
20.9 m
7) r = 9 ft, θ =
7π
4
8) r = 14 ft, θ =
49.5 ft
19π
12
69.6 ft
Find the length of each arc. Do not round.
9)
10)
315°
150°
19 ft
8 cm
95π
ft
6
14π cm
12)
11)
3π
4
π
2
13 ft
14 cm
39π
ft
4
7π cm
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-1-
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra
Name___________________________________
Coterminal Angles and Reference Angles
Date________________ Period____
Find the reference angle.
2)
1)
y
y
x
x
25π
−
18
−230°
3)
4)
y
y
−
29π
18
x
x
7π
−
9
5)
6)
y
y
31π
9
x
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x
640°
-1-
Worksheet by Kuta Software LLC
7) −510°
9) −
13π
12
8) −
19π
18
10) −250°
State if the given angles are coterminal.
11) 185°, −545°
12)
17π 161π
,
36
36
Find a coterminal angle between 0° and 360°.
13) −330°
14) −435°
15) 640°
16) −442°
Find a coterminal angle between 0 and 2π for each given angle.
17)
11π
3
18) −
35π
18
19)
15π
4
20) −
19π
12
Find a positive and a negative coterminal angle for each given angle.
21)
5π
4
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22)
-2-
25π
36
Worksheet by Kuta Software LLC
Kuta Software - Infinite Algebra
Name___________________________________
Coterminal Angles and Reference Angles
Date________________ Period____
Find the reference angle.
2)
1)
y
y
x
x
25π
−
18
−230°
50°
7π
18
3)
4)
y
y
−
29π
18
x
x
7π
−
9
2π
9
7π
18
5)
6)
y
y
31π
9
x
x
640°
80°
4π
9
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-1-
Worksheet by Kuta Software LLC
7) −510°
8) −
30°
9) −
13π
12
19π
18
π
18
10) −250°
70°
π
12
State if the given angles are coterminal.
11) 185°, −545°
12)
No
17π 161π
,
36
36
Yes
Find a coterminal angle between 0° and 360°.
13) −330°
14) −435°
30°
15) 640°
285°
16) −442°
278°
280°
Find a coterminal angle between 0 and 2π for each given angle.
17)
11π
3
18) −
5π
3
19)
15π
4
35π
18
π
18
20) −
7π
4
19π
12
5π
12
Find a positive and a negative coterminal angle for each given angle.
21)
5π
4
22)
13π
3π
and −
4
4
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25π
36
97π
47π
and −
36
36
-2-
Worksheet by Kuta Software LLC