Angles and Angle Measure

Learn how to convert degrees to radians or radians to degrees by following a step-by-step guide.

Step by step guide to solve angles and angle measure problems

• To convert degrees to radians, use this formula: $$\color{blue}{Radians = Degrees \ × \frac{π}{180}}$$
• To convert radians to degrees, use this formula: $$\color{blue}{Degrees =Radians ×\frac{180}{π}}$$

Example 1:

Convert $$120$$ degrees to radians.

Solution:

Use this formula: Radians $$=$$ Degrees $$×\frac{π}{180}$$
Radians $$=120×\frac{π}{180}=\frac{120π}{180}=\frac{2π}{3}$$

Example 2:

Convert $$\frac{\pi}{3}$$ to degrees.

Solution:

Use this formula: Degrees $$=$$ Radians $$×\frac{180}{π}$$
Radians $$=\frac{π}{3}×\frac{180}{π}=\frac{180π}{3π}=60$$

Example 3:

Convert $$150$$ degrees to radians.

Solution:

Use this formula: Radians $$=$$ Degrees $$×\frac{π}{180}$$
Radians $$=150×\frac{π}{180}=\frac{150π}{180}=\frac{5π}{6}$$

Example 4:

Convert $$\frac{2π}{3}$$ to degrees.

Solution:

Use this formula: Degrees $$=$$ Radians $$×\frac{ 180}{ π }$$
Radians $$=\frac{2π}{3}×\frac{180}{π}=\frac{360π}{3π}=120$$

Exercises

Convert each degree measure into radians and convert each radian measure into degrees.

• $$\color{blue}{-150^\circ}$$
• $$\color{blue}{420^\circ}$$
• $$\color{blue}{300^\circ}$$
• $$\color{blue}{\frac{5π}{9}=}$$
• $$\color{blue}{-\frac{π}{3}=}$$
• $$\color{blue}{\frac{13π}{6}=}$$

• $$\color{blue}{-\frac{5π}{6}}$$
• $$\color{blue}{\frac{7π}{3}}$$
• $$\color{blue}{\frac{5π}{3}}$$
• $$\color{blue}{100^\circ}$$
• $$\color{blue}{-60^\circ}$$
• $$\color{blue}{390^\circ}$$