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A protractor is a measuring instrument, typically made of transparent plastic, for measuring angles. Some protractors are simple half-discs or full circles. More advanced protractors, such as the bevel protractor, have one or two swinging arms, which can be used to help measure the angle. Most protractors measure angles in degrees (°).
The sum of the angles equals 90 degrees (22.5° +67.5°= 90°). It is also obvious from a visual check when using a protractor that where the instruments displays 22.5° is actually 67.5° on the protractor. Many newer slide miters and miter boxes display both angles. Some of the new calculators have a 0° and a 90° references.
The group of constructible angles is closed under the operation that halves angles (which corresponds to taking square roots in the complex numbers). The only angles of finite order that may be constructed starting with two points are those whose order is either a power of two, or a product of a power of two and a set of distinct Fermat primes ...
Greek astronomers used the dioptra to measure the positions of stars; both Euclid and Geminus refer to the dioptra in their astronomical works. It continued in use as an effective surveying tool. Adapted to surveying, the dioptra is similar to the theodolite , or surveyor's transit, which dates to the sixteenth century.
Therefore, both angle A and angle B have measures equal to x and are equal in measure. Angles A and B are adjacent. Adjacent angles, often abbreviated as adj. ∠s, are angles that share a common vertex and edge but do not share any interior points. In other words, they are angles side by side or adjacent, sharing an "arm".
A square is a tool used for marking and referencing a 90° angle, though mitre squares are used for 45° angles. Squares see common use in woodworking, metalworking, construction and technical drawing. [1] Some squares incorporate a scale for measuring distances (a ruler) or for calculating angles.
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