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All right angles are equal to each other. If two straight lines in a plane are crossed by another straight line (called the transversal), and the interior angles between the two lines and the transversal lying on one side of the transversal add up to less than two right angles, then on that side of the transversal, the two lines extended will ...
An angle larger than a straight angle but less than 1 turn (between 180° and 360°) is called a reflex angle. An angle equal to 1 turn (360° or 2 π radians) is called a full angle, complete angle, round angle or perigon. An angle that is not a multiple of a right angle is called an oblique angle.
The chord of an angle subtends the arc of the angle. Ancient Greek and Hellenistic mathematicians made use of the chord. Given a circle and an arc on the circle, the chord is the line that subtends the arc. A chord's perpendicular bisector passes through the center of the circle and bisects the angle.
Angles whose sum is a right angle are called complementary. Complementary angles are formed when a ray shares the same vertex and is pointed in a direction that is in between the two original rays that form the right angle. The number of rays in between the two original rays is infinite. Angles whose sum is a straight angle are supplementary ...
At roughly the same time, the Han Chinese and the Romans both invented the wheeled odometer device for measuring distances traveled, the Roman model first described by the Roman civil engineer and architect Vitruvius (c. 80 BC – c. 15 BC). [102] The device was used at least until the reign of emperor Commodus (r.
Explicitly, they are defined below as functions of the known angle A, where a, b and h refer to the lengths of the sides in the accompanying figure. In the following definitions, the hypotenuse is the side opposite to the 90-degree angle in a right triangle; it is the longest side of the triangle and one of the two sides adjacent to angle A.
For many practical purposes, a degree is a small enough angle that whole degrees provide sufficient precision. When this is not the case, as in astronomy or for geographic coordinates (latitude and longitude), degree measurements may be written using decimal degrees (DD notation); for example, 40.1875°.
Thales was a philosopher, scientist, mathematician, and engineer, [60] also known for a special case of the inscribed angle theorem. Pythagoras's birthplace, the island of Samos , is situated in the Northeast Aegean Sea not far from Miletus . [ 61 ]