A protractor is a device for measuring the angle between two intersecting lines. The angle is measured in degrees, and a circle is defined as having 360 degrees of identical size. The earliest known protractors were designed in the 17th century by sailors needing to plot courses on nautical charts.
A basic protractor consists of a half-circular piece of material with degree markings notched onto the outside edge of the arc, or curved section. The straight edge is placed along one of the lines to be measured, and the number of degrees is determined by where the second line crosses the arc.
Because it is a half-circle, the basic protractor only measures angles up to 180 degrees. This is adequate in normal use, as the relationship between two lines can always be expressed as an angle of 180 degrees or less. If the original placement of the protractor produces an angle greater than 180 degrees, simply flipping it over will provide a reading of less than 180 degrees.
This is due to the symmetrical nature of the circle; starting from one line, the angle to a second intersecting line can be measured by moving either clockwise or counter clockwise. One direction will measure an angle greater than 180 degrees, and the other will measure an angle less than 180 degrees. They cannot both measure more than 180, as they must add up to 360, the number of degrees in a full circle.
An alternate type of protractor is made from two straight edges attached to each other at one end, with a graduated arc between them. The arc is attached to one arm, and the other arm slides freely over it. An arm is placed along one line, and the other arm is swung outwards until it is parallel to the other line. The degrees are then read off the arc. Astronomers often use a third type of protractor, one formed from a fully circular piece of material. This allows them to directly measure all angles between 0 and 360.
Protractors are generally used for measuring existing lines, but they can also be constructed to help draw them. By attaching a swiveling arm to the straight edge of the semicircular disk described above, lines with arbitrary angles can be drawn. Such devices are most commonly used in drafting of technical drawings such as architectural plans.