How to Write Each Measure in Degrees

How to Write Each Measure in Degrees

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The angle of an arc in a circle that is produced by wrapping the circle's radius around its circumference is known as a radian. We use radians and degrees to indicate the angle between two lines. A circle has a total angle of \(360\) degrees or \(2π\) radians. Angles expressed in radians can be translated into degrees using radians to degrees.

Radians to Degrees Formula

Degree \(=\) Radian \(\times \ \frac{180}{π}\)

Example

Convert \(\frac{3π}{2}\) radians to degrees.

Solution:

\(\frac{3π}{2} \ \times \ \frac{180}{π} \ = \ \frac{180 \times 3π}{2π} \ = \ 270°\)

Free printable Worksheets

Exercises for Writing Each Measure in Degrees

1) Find the answer: \(\frac{22π}{9} \ =\)

2) Find the answer: \(\frac{15π}{8} \ =\)

3) Find the answer: \(\frac{25π}{6} \ =\)

4) Find the answer: \(\frac{31π}{5} \ =\)

5) Find the answer: \(-\frac{5π}{9} \ =\)

6) Find the answer: \(-\frac{16π}{3} \ =\)

7) Find the answer: \(\frac{13π}{5} \ =\)

8) Find the answer: \(\frac{13π}{5} \ =\)

9) Find the answer: \(\frac{25π}{12} \ =\)

10) Find the answer: \(\frac{14π}{9} \ =\)

 

1) Find the answer: \(\frac{22π}{9} \ =\)

\(\color{red}{\frac{22π}{9} \ = \ \frac{22π}{9} \times \frac{180}{π} \ = \ 440°}\)

2) Find the answer: \(\frac{15π}{8} \ =\)

\(\color{red}{\frac{15π}{8} \ = \ \frac{15π}{8} \times \frac{180}{π} \ = \ 337.5°}\)

3) Find the answer: \(\frac{25π}{6} \ =\)

\(\color{red}{\frac{25π}{6} \ = \ \frac{25π}{6} \times \frac{180}{π} \ = \ 750°}\)

4) Find the answer: \(\frac{31π}{5} \ =\)

\(\color{red}{\frac{31π}{5} \ = \ \frac{31π}{5} \times \frac{180}{π} \ = \ 1116°}\)

5) Find the answer: \(-\frac{5π}{9} \ =\)

\(\color{red}{-\frac{5π}{9} \ = \ -\frac{5π}{9} \times \frac{180}{π} \ = \ -100°}\)

6) Find the answer: \(-\frac{16π}{3} \ =\)

\(\color{red}{-\frac{16π}{3} \ = \ -\frac{16π}{3} \times \frac{180}{π} \ = \ -960°}\)

7) Find the answer: \(\frac{13π}{5} \ =\)

\(\color{red}{\frac{13π}{5} \ = \ \frac{13π}{5} \times \frac{180}{π} \ = \ 468°}\)

8) Find the answer: \(\frac{13π}{5} \ =\)

\(\color{red}{\frac{13π}{5} \ = \ \frac{13π}{5} \times \frac{180}{π} \ = \ 468°}\)

9) Find the answer: \(\frac{25π}{12} \ =\)

\(\color{red}{\frac{25π}{12} \ = \ \frac{25π}{12} \times \frac{180}{π} \ = \ 375°}\)

10) Find the answer: \(\frac{14π}{9} \ =\)

\(\color{red}{\frac{14π}{9} \ = \ \frac{14π}{9} \times \frac{180}{π} \ = \ 280°}\)

Writing Each Measure in Degrees Practice Quiz