How can we draw a 60 degree angle without any protacter?

This page shows how to construct (draw) a 60 degree angle with compass and straightedge or ruler. This construction works by creating an equilateral triangle. Recall that an equilateral triangle has all three interior angles 60°. We use one of those angles to get the desired 60 degree result. See the proof below for more details.

Step-by-step Instructions |

After doing this | |
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1. Draw a line segment which will become one side of the angle. (Skip this step if you are given this line.) The exact length is not important. Label it PQ. P will be the angle's vertex. | |

2. Set the compass on P, and set its width to any convenient setting. | |

3. Draw an arc across PQ and up over above the point P. | |

4. Without changing the compass width, move the compass to the point where the arc crosses PQ, and make an arc that crosses the first one. | |

5. Draw a line from P, through the intersection of the two arcs. | |

6. Done. The angle QPR has a measure of 60° |

## Proof

This construction works by creating an equilateral triangle. Recall that an equilateral triangle has all three interior angles 60°. The image below is the final drawing above with the red items added.

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