# How to Solve Angles and Angle Measure? (+FREE Worksheet!)

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

## Related Topics

- How to Evaluate Trigonometric Function
- How to Find Missing Sides and Angles of a Right Triangle
- How to Solve Coterminal Angles and Reference Angles
- How to Solve Trig Ratios of General Angles

## 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: \(\color{blue}{Degrees =Radians ×\frac{180}{π}}\)

### Angles and Angle Measure – Example 1:

Convert \(120\) degrees to radians.

**Solution:**

Use this formula: \(Radians\) \(=\) \(Degrees\) \(×\frac{π}{180}\)

Radians \(=120×\frac{π}{180}=\frac{120π}{180}=\frac{2π}{3}\)

### Angles and Angle Measure – Example 2:

Convert \(\frac{\pi}{3}\) to degrees.

**Solution**:

Use this formula: \(Degrees\) \(=\) \(Radians\) \(×\frac{180}{π}\)

Radians \(=\frac{π}{3}×\frac{180}{π}=\frac{180π}{3π}=60\)

### Angles and Angle Measure – Example 3:

Convert \(150\) degrees to radians.

**Solution**:

Use this formula: \(Radians\) \(=\) \(Degrees\) \(×\frac{π}{180}\)

Radians \(=150×\frac{π}{180}=\frac{150π}{180}=\frac{5π}{6}\)

### Angles and Angle Measure – 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 for Solving Angles and Angle Measure

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

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

### ِِِِDownload Angles and Angle Measure Worksheet

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

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