Angle (geometry)

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Fig. 1. An acute angle showing terminology: arms (red), vertex (blue), and angle (green)

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 2πr, 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.

[edit] Types

There are various special types of angles.

Fig. 2 Right angle.
Fig. 3 An obtuse angle
Fig. 4 A straight angle

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.

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