An angle is a measure of rotation or turning. In geometry, it is the figure formed by two rays, known as the sides of the angle, sharing a common endpoint, called the vertex. The size of an angle is determined by the amount of rotation needed to align one ray with the other.
Angles are usually measured in degrees or radians. A full rotation is 360 degrees or 2π radians. The degree is typically used in the everyday world (such as for measuring angles in a circle or a triangle), while the radian is the standard unit of angular measure in mathematics and many scientific fields.
Angles can be classified based on their measure. An angle measuring exactly 90 degrees is a right angle. Angles less than 90 degrees are called acute angles, and those more than 90 degrees but less than 180 degrees are obtuse angles. An angle of exactly 180 degrees is a straight angle, while an angle of more than 180 degrees but less than 360 degrees is a reflex angle.
A perpendicular angle is equal to a quarter of a full rotation. A perpendicular angle is measured as 90 degrees or 1/4 τ radians.
An acute angle is an angle that measures less than 90 degrees.
An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees. It is larger than a right angle and smaller than a straight angle.
A reflex angle is an angle whose measure is greater than 180 degrees but less than 360 degrees.
A radian angle is measured by the ratio of the angle's arc length over the radius of a circle. A full rotation in radians is equal to τ (tau) radians.
Degrees are a unit of measurement for angles, representing the rotation between two rays. The degree angle system divides a full rotation into 360 units called degrees.