## How to Write Each Measure in Degrees

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.

Degree $$=$$ Radian $$\times \ \frac{180}{π}$$

### Example

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

Solution:

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

### 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

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