# Measuring angles in degrees

## In a nutshell

An angle is formed when two lines meet at a shared point. Angles are measured in degrees ($\degree$), which can be measured with a protractor.

## Angles and measurement

The degree ($\degree$) is the unit of measurement for angles. There are $90\degree$ in a right angle, and $360\degree$ in a full circle. A protractor is a tool used to measure how many degrees are in an angle.

## Acute angles

Here are the steps for how to measure an acute angle with a protractor:

#### Procedure

1. | Place the midpoint of the protractor on the vertex of the angle. |

2. | Line up one side of the angle with the zero line of the protractor (where the number $0$ appears). |

3. | Read the degrees where the other side of the angle crosses the number scale. |

*In the example above, the acute angle has a measurement of *$\underline{40\degree}$.

## Obtuse angles

Here are the steps for how to measure an obtuse angle with a protractor:

#### Procedure

1. | Place the midpoint of the protractor on the vertex of the angle. |

2. | Line up one side of the angle with the zero line of the protractor (where the number $0$ appears). |

3. | Read the degrees of the other side of the angle, and subtract this value from $90\degree$. |

4. | Add the $90\degree$ to the previous value to find the overall obtuse angle. |

*In the example above, the obtuse angle has a measurement of *$\underline{110\degree}$ *because*:

$(90\degree - 70\degree) + 90\degree = \underline{110 \degree}$

## Reflex angles

Here are the steps for how to measure a reflex angle with a protractor:

#### Procedure

1. | Place the midpoint of the protractor on the vertex of the angle. |

2. | Measure the smaller angle on the other side of the reflex angle, with the same method as described above for an obtuse angle. |

3. | Subtract this smaller angle from $360\degree$ to give the value of the reflex angle. |

*In the example above, the reflex angle has a measurement of *$\underline{320\degree}$ because:

$360\degree-40\degree=\underline{320\degree}$