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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 (°).
In trigonometry, the gradian – also known as the gon (from Ancient Greek γωνία (gōnía) 'angle'), grad, or grade [1] – is a unit of measurement of an angle, defined as one-hundredth of the right angle; in other words, 100 gradians is equal to 90 degrees.
These four are: the Unique line assumption (which was called the Point-Line Postulate by Birkhoff), the Number line assumption, the Protractor postulate (to permit the measurement of angles) and an axiom that is equivalent to Playfair's axiom (or the parallel postulate).
Postulate III: Postulate of angle measure. The set of rays { ℓ, m, n , ...} through any point O can be put into 1:1 correspondence with the real numbers a (mod 2 π ) so that if A and B are points (not equal to O ) of ℓ and m , respectively, the difference a m − a ℓ (mod 2π) of the numbers associated with the lines ℓ and m is ∠ AOB .
Measuring the slope angle of a tape or chain during distance measurement. Measuring the height of a building, tree, or other feature using a vertical angle and a distance (determined by taping or pacing), using trigonometry. Measuring the angle of drilling in well logging. Measuring the list of a ship in still water and the roll in rough water.
Since angle B is supplementary to both angles C and D, either of these angle measures may be used to determine the measure of Angle B. Using the measure of either angle C or angle D, we find the measure of angle B to be 180° − (180° − x) = 180° − 180° + x = x. Therefore, both angle A and angle B have measures equal to x and are equal ...
Many angle units are defined as a division of the turn. For example, the degree is defined such that one turn is 360 degrees. Using metric prefixes, the turn can be divided in 100 centiturns or 1000 milliturns, with each milliturn corresponding to an angle of 0.36°, which can also be written as 21′ 36″.
A circle marked off in 15° angles is needed (circular protractor). An arbitrary point on the sub-style line is chosen. From here, a long-line, at right-angles to it, is drawn. A line is drawn at right angles from the substyle height, so that it passes through that point. Its length is noted. The length is copied from the point to O'.
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