# Angle (geometry)

In Euclidean geometry, an **angle** is the figure formed by two straight intersecting lines. The point at which the lines intersect is called the **vertex** of the angle. The parts of the lines that extend from the vertex and surround the angle are called the arms.

An angle is measured in degrees (one degree is 1/360-th part of the circumference of a circle of unit radius). Degrees are usually indicated by a circle superscript, for instance, 45°.

An angle can also be measured in radians. The circumference of a circle with radius *r* is of length 2π*r*, where π is a mathematical constant approximately equal to 3.14. If *c* is the length of arc spanning an angle, then the magnitude of the angle is equal to *c/r* radians, which is equal to [360/(2π)]⋅*c/r* = *c/r*⋅180/π degrees.

## Types

There are various special types of angles.

A **right angle** is an angle of 90° = 90⋅(π/180) = π/2 radians.
A right angle divides a circle in four equal parts. See Fig. 2.

An **obtuse angle** α has a magnitude greater than a right angle, but less than a straight angle, 90° < α < 180°. See Fig. 3.

An **acute angle** is one where the magnitude of the angle α is less than a right angle, 90° > α > 0°. See Fig.1

A **straight angle** is the angle formed by a straight line. Its magnitude is equal to the sum of two right angles, α = 180°. See Fig. 4.