Angle

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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.


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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.

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 grad.

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 $180^\circ=\pi\; rad$.

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$\Leftrightarrow 90^\circ<m\angle ABC<180^\circ$.