angle

My geometry teacher was sometimes acute, and sometimes obtuse, but he was always right.

—anonymous

In plane geometry, an angle id the opening between two lines or two planes that meet; the word comes from the Latin angulus for a sharp bend. Plane angles are measured in degrees or radians.

A right angle has exactly 90° (or π/2 radians), an acute angle less than 90°, an obtuse angle has between 90° and 180°, and a straight angle has exactly 180°. Any angle that is at most 180° is said to be convex. An angle between 180° and 360° is called a reflex angle. An angle of exactly 360° is said to be a full angle. Complementary angles add to give 90°, supplementary angles make a total of 180°.

In spherical geometry, a spherical angle is that formed by intersecting arcs of two great circles; its magnitude is equal to that of the angle between the two planes of the great circles.

See also solid angle.

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• GEOMETRY

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