angledegrees

Angle degrees, commonly denoted with the symbol °, are a unit for measuring the size of an angle. One degree is defined as 1/360 of a full circle, so a circle comprises 360 degrees. The term degrees can be abbreviated as deg in some contexts.

Key reference angles include 90° (a right angle), 180° (a straight angle), and 360° (a full angle). Angles are often described as acute (<90°), obtuse (90°–<180°), or reflex (≥180° and <360°). Angles can also be measured in clockwise or counterclockwise directions, with standard mathematical practice often taking positive angles counterclockwise from the positive x-axis.

Conversion between degrees and radians: radians = degrees × π / 180, degrees = radians × 180 / π. In computations, arc length s = rθ and area of a sector A = (π r^2)(θ/360) when θ is in degrees; with θ in radians, s = rθ and A = (1/2)r^2θ.

Subdivisions: 1 degree = 60 arcminutes; 1 arcminute = 60 arcseconds. Decimal degrees express fractions of a degree, such as 12.5°. For higher precision, angle measurements may use sexagesimal or decimal formats.

Applications: angle degrees are used in geometry, trigonometry, surveying, astronomy, navigation, architecture, and computer graphics. The concept has historical roots in the sexagesimal system developed by ancient civilizations; today degrees are standardized and widely supported in measurement and computation.