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converting degrees to radians and vice versa - Printable Mathematics Worksheets - Wayground

converting degrees to radians and vice versa

12 questions

10th - 11th Grade

Mathematics

This free printable mathematics worksheet helps students in Grades 10–11 convert angle measures between degrees and radians. Its 12 multiple-choice questions include degree-to-radian conversions such as 100°, 110°, 150°, 225°, 255°, and 270°, as well as radian-to-degree conversions involving fractions of π, including 2π/3, 7π/4, 3π/4, 5π/3, and 10π/9. The worksheet also checks students’ understanding that one radian is approximately 57.3°, helping them connect exact angle measures with a useful approximation. Students must select simplified fractional-π answers and identify equivalent degree measures, reinforcing the conversion relationship 180° = π radians and supporting Algebra II and Geometry practice. It is suitable for independent practice, homework, review, or a quick formative check. The free printable worksheet includes a complete answer key for efficient checking.

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Worksheets

converting degrees to radians and vice versa

Total questions: 12

Name
Class
Date
1.

What is  225°225\degree  in radians? 

a)

 7π4\frac{7\pi}{4}  

b)

 5π4\frac{5\pi}{4}  

c)

 3π4\frac{3\pi}{4}  

d)

 5π3\frac{5\pi}{3}  

2.

What is \frac{2\pi}{3}   radians in degrees? 

a)

150

b)

120

c)

180

d)

 30

3.

What is  7π4\frac{7\pi}{4}   radians in degrees?


a)

300

b)

135

c)

315

d)

45

4.
Convert 150⁰ to radians
a)
5π/6
b)
3π/4
c)
7π/6
d)
2π/3
5.

What is  270°270\degree  in radians?

a)

π4\frac{\pi}{4}

b)

3π2\frac{3\pi}{2}

c)

3π4\frac{3\pi}{4}

d)

π2\frac{\pi}{2}

6.

Convert 100⁰ to radians

a)


5π9\frac{5\pi}{9}

b)

π2\frac{\pi}{2}

c)

5π8\frac{5\pi}{8}

d)

5π6\frac{5\pi}{6}

7.

Convert  110°110\degree  into radians

a)

 5π3\frac{5\pi}{3}  

b)

 3π4\frac{3\pi}{4}  

c)

 11π18\frac{11\pi}{18}  

d)

 11π9\frac{11\pi}{9}  

8.

Convert  255°255\degree  into radians

a)

 5π3\frac{5\pi}{3}  

b)

 9π4\frac{9\pi}{4}  

c)

 25π18\frac{25\pi}{18}  

d)

 17π12\frac{17\pi}{12}  

9.

convert  3π4\frac{3\pi}{4}  rad into degrees

a)

 135°135\degree  

b)

 140°140\degree  

c)

 175°175\degree  

d)

 210°210\degree  

10.

convert  5π3\frac{5\pi}{3}  rad into degrees

a)

 210°210\degree  

b)

 300°300\degree  

c)

 270°270\degree  

d)

 315°315\degree  

11.

convert  10π9\frac{10\pi}{9}  rad into degrees

a)

 200°200\degree  

b)

 190°190\degree  

c)

 230°230\degree  

d)

 245°245\degree  

12.

Approximately how many degrees is 1 radian?

a)

50°50\degree

b)

57.3°57.3\degree

c)

60°60\degree

d)

63.5°63.5\degree

Answer Key

converting degrees to radians and vice versa

Total questions: 12

1.
b)

 5π4\frac{5\pi}{4}  

2.
b)

120

3.
c)

315

4.
a) 5π/6
5.
b)

3π2\frac{3\pi}{2}

6.
a)


5π9\frac{5\pi}{9}

7.
c)

 11π18\frac{11\pi}{18}  

8.
d)

 17π12\frac{17\pi}{12}  

9.
a)

 135°135\degree  

10.
b)

 300°300\degree  

11.
a)

 200°200\degree  

12.
b)

57.3°57.3\degree

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FAQs

What does this degrees-to-radians and radians-to-degrees worksheet cover?

This Grade 10–11 mathematics worksheet covers converting exact angle measures between degrees and radians using 180° = π radians. Its 12 multiple-choice questions require students to select simplified fractional-π forms for degree measures and equivalent degree values for radian measures, with an additional item on the approximation 1 radian ≈ 57.3°.

How can I teach degree-to-radian and radian-to-degree conversions with this worksheet?

Begin by reviewing the equivalence 180° = π radians and model multiplying by π/180 to convert degrees or by 180/π to convert radians. Then have students explain how a measure such as 150° becomes 5π/6 and how 7π/4 becomes 315° before completing the multiple-choice items. Use the answer choices to discuss why unreduced or mismatched fractions are incorrect.

What mistakes should I watch for on this angle-conversion worksheet?

Students may use the wrong conversion factor, treating π radians as 360° instead of 180°, or reverse the factors for a conversion. They may also fail to simplify results, confuse nearby fractional-π values such as 3π/4 and 5π/4, or select 57.3° as an exact conversion rather than the approximate value of 1 radian. Check that students label whether each question begins with degrees or radians before calculating.

How do I assign and grade this worksheet?

You can assign this degrees-and-radians worksheet as a printable PDF or as a digital quiz on Wayground. It includes a complete answer key for all 12 multiple-choice questions, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable format also gives schools an option for reducing screen time.

How can I differentiate this degrees-and-radians worksheet for my students?

Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size so the degree symbols, π fractions, and multiple-choice options are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when those changes support access to the conversion practice.

Where can I find more free worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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