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.
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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 \(=120×\frac{π}{180}=\frac{120π}{180}=\frac{2π}{3}\)
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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 \(=150×\frac{π}{180}=\frac{150π}{180}=\frac{5π}{6}\)
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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.
- \(\color{blue}{-150^\circ}\)
- \(\color{blue}{420^\circ}\)
- \(\color{blue}{300^\circ}\)
- \(\color{blue}{\frac{5π}{9}=}\)
- \(\color{blue}{-\frac{π}{3}=}\)
- \(\color{blue}{\frac{13π}{6}=}\)
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- \(\color{blue}{-\frac{5π}{6}}\)
- \(\color{blue}{\frac{7π}{3}}\)
- \(\color{blue}{\frac{5π}{3}}\)
- \(\color{blue}{100^\circ}\)
- \(\color{blue}{-60^\circ}\)
- \(\color{blue}{390^\circ}\)
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