Angle

Definition

An angle is the union of two rays with a common endpoint. The common endpoint of the rays is called the vertex of the angle, and the rays themselves are called the sides of the angle. If a ray is drawn between the two rays, it is called the angle bisector of the angle.

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There are many notations for angles. The most common form is $\angle ABC$ , read "angle ABC", where $A,C$ are points on the sides of the angle and $B$ is the vertex of the angle. Note that the same angle can be denoted many different ways by choosing different points along the side of the angle.

Angle Measure

The measure of $\angle ABC$ is denoted $m\angle ABC$ , read "measure of angle ABC". There are three units for measuring angles: degrees, radians, and gradians.

Special Angles

Straight Angle

A straight angle is an angle formed by a pair of opposite rays, or a line. A straight angle has a measure of $180^\circ=\pi\; \mathrm{ rad}$ .

Right Angle

A right angle is an angle that is supplementary to itself. A right angle has a measure of $90^\circ=\frac{\pi}{2}\; rad$ .

An acute angle has a measure greater than zero but less than that of a right angle, i.e. $\angle ABC$ is acute $\Leftrightarrow 0^\circ<m\angle ABC<90^\circ$ .

An obtuse angle has a measure greater than that of a right angle but less than that of a straight angle, i.e. $\angle ABC$ is obtuse $\Leftrightarrow 90^\circ<m\angle ABC<180^\circ$ .

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