What instrument measures angles?

A protractor, compass, speed square, goniometer, theodolites, sextant, or angle finder can be used to measure angles.

A protractor is a circular or semi circular instrument for measuring angles and some have existed from ancient times. A half circular protractor is marked for 180 degrees and a full circle for 360 degrees. Protractors usually have two sets of numbers going in opposite directions, so be careful which side you use. When in doubt you should ask yourself is the angle greater or smaller that 90 degrees.

An inclinometer measures the slope (aka grade or "incline") on mountain roads and trails.

Practice lining up and reading a protractor while you measure a set of angles in this fun learning activity. The angles may range from 0° to 180°. The interactive protractor is already lined up with the vertex of each angle but you will have to rotate the protractor into proper position. The margin of error is only 1° and you must report measurement to the nearest whole number.

A protractor measures angles whereas a compass draws angles.

The typical protractor is 180 degrees. Protractors can also be circular and measure up to a full 360 degrees. Other methods of measuring angles include using a compass, and length measuring devices (rulers, tape measures, etc.) combined with trigonometry. Estimated angle measures can also use "devices." For example, the corner of a page can tell you if an angle is greater than or less than 90 degrees.

Navigators in the old days would use a sextant for measuring angles. In more recent times they used a transit. A quadrant is yet another tool for measuring the angle between the horizon and heavenly bodies, also useful for navigation.
A protractor can be used to measure an angle.