Angle

Angle, in plane geometry, the figure formed by the intersection of two straight lines. The point of intersection is known as the vertex. If the two lines are viewed as radii of a circle of unit radius, the magnitude of an angle can be defined in terms of the proportion of the circle's circumference cut off by the two lines. Angles are measured in radians or degrees. One radian is the magnitude of an angle whose two sides cut off an arc of circumference equal in length to the radius. A degree is the magnitude of an angle whose two sides cut off 1/360 of the circumference. An angle of π/2 rad (90°), whose sides cut off one-quarter of the circumference, is a right angle, the two lines being said to be perpendicular. An angle of π rad, or 180°, whose sides cut off one-half of the circumference, is a straight angle or straight line. Angles less than 90° are termed acute; those greater than 90° but less than 180°, obtuse; greater than 180°, reflex. Pairs of angles that add up to 90° are complementary; those that add up to 180°, supplementary. In solid geometry, angles have definitions that are specific to the solids.

See also: Geometry; Trigonometry.