Using the correct tool for measuring angles depends on the project. For geometry, architectural drawings and drafting, a protractor or compass may be used. Construction workers use mitre gauges to measure angles and mitre saws to cut angles. For celestial navigation, a sextant is used to measure the angle between the stars---or some other object---and the horizon. Land surveyors use a theodolite to measure angles while mapping the terrain.
The compass can be used to create a perpendicular bisector, or a 45-degree angle. First a straight, horizontal line is drawn. Then the compass is stretched to the line's centre point. From one end of the line, the compass is swivelled to draw a mark above and below the line. This is repeated from the opposite end of the horizontal line. Two marks above the horizontal line should cross as will the two marks below it. By lining up a straight edge with the crossed marks above and below the horizontal line, and drawing a vertical line though them, a 45-degree angle is created.
Protractors are used by first lining up the straight edge with an horizontal line of an angle. Next the other edge of the angle is examined to find where it extends along the curved edge. The degree measurement can be read---up to 180-degrees---along this curved outer edge. Acute angles measure less than 90 degrees, right angles equal 90 degrees, and obtuse angles fall between 90 and 180 degrees.
Sextants measure angles by lining up the bottom arm with the horizon and the upper arm with a predetermined object like a star or the sun. Using the angle, the celestial object's name, along with the known date and time, and comparing the information to annual navigational almanac charts that record this information, any sea or land navigator can accurately find their location.
Theodolites measure horizontal and vertical angles mainly for surveying purposes, but they have been adapted for meteorology and rocket-launching technology. The instrument is aimed at a target object. Then a telescope is adjusted vertically and horizontally to line it up with the object. Angles can then be accurately determined.
Mitre Gauge and Miter Saw
Construction workers and engineers use a hinged mitre gauge to measure inside and outside angles around corners. The angle is read around the outside of the hinged joint. Once the angle is determined, floor and crown moulding, as well as wood or tile flooring, can be cut with a mitre saw adjusted to the correct angle.