How to Solve Angles and Angle Measure

How to Solve 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: \(\color{blue}{Degrees =Radians ×\frac{180}{π}}\)

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

Answers

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

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