Protractor

Protractors are used for a few different tasks and crafting a Measuring Sledgehammer.

Mr. Math
If Mr. Math is given a protractor, he will stand still and eat it. He will not eat another Protractor until 20 seconds have passed. Doing this doesn't appear to have a purpose besides wasting a useful Item.

Knock Out Robert or Principal Failure
You can craft a Protractor with a Ruler to make a Measuring Sledgehammer. With this hammer, you can bonk Robert on the head so he stops trying to lick you. This will make him slide backwards into a wall and sit there for 40 seconds. You can hit Principal Failure with it to stop her from moving for 20 seconds.

Kill Ann
If you show Ann the Measuring Sledgehammer, she will have a stroke and die. She will be alive again the next game, but keep in mind she'll stay dead for the whole game. This also means you cannot get the Stapler Gun if you killed her before you got it.

Distracting Keisha
If Keisha is about to report you, use the Protractor to make her stop so you can run away.