angle

angle, in mathematics, figure formed by the intersection of two straight lines; the lines are called the sides of the angle and their point of intersection the vertex of the angle. Angles are commonly measured in degrees (°) or in radians. If one side and the vertex of an angle are fixed and the other side is rotated about the vertex, it sweeps out a complete circle of 360° or 2π radians with each complete rotation. Half a rotation from 0° or 0 radians results in a straight angle, equal to 180° or π radians; the sides of a straight angle form a straight line. A quarter rotation (half of a straight angle) results in a right angle, equal to 90° or π/2 radians; the sides of a right angle are perpendicular to one another. An angle less than a right angle is acute, and an angle greater than a right angle is obtuse. Two angles that add up to a right angle are complementary. Two angles that add up to a straight angle are supplementary. One of the geometric problems of antiquity is the trisection of an angle. Angles can also be formed by higher–dimensional figures, as by a line and a plane, or by two intersecting planes.

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angle

In geometry, a pair of rays (see line) sharing a common endpoint (the vertex). An angle may be thought of as the rotation of a single ray from an initial to a terminal position. Clockwise rotation is considered negative and counterclockwise rotation positive. Either may be measured in degrees (one full rotation = 360°) or radians (one full rotation = 2π rad). A 90° angle is called a right angle. Any angle less than 90° is an acute angle. Any angle more than 90° but less than 180° is an obtuse angle.

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Angle

Any member of a Germanic people who, with the Jutes and Saxons, invaded England in the 5th century AD. According to Bede, their homeland was Angulus, traditionally identified as the Angeln district in Schleswig. They abandoned this area when they invaded Britain, where they settled in the kingdoms of Mercia, Northumbria, East Anglia, and Middle Anglia. Their language was known, even then, as Englisc, and they gave their name to England.