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.

The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2012, Columbia University Press. All rights reserved.

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