From the Super Mario Wiki, the Mario encyclopedia
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The Protractor is a souvenir located in the Doodads folder in WarioWare: Twisted! The Protractor displays an angle (from a total of 360°) based on how much the console is tilted. Unlike the other doodads, it looks strikingly different than a regular protractor, sporting a futuristic look instead. It is used in order to measure angles. If is pressed, the displayed angle is reset back to 0°.