Angles
Notation
Angles are notated by \(\angle B\) or \(\angle1\) or \(\angle ABC\), which would depend on the marking on the diagram. Typically the letter of the relevant vertex is used.
Anatomy
An angle is comprised of two sides, which join at a common vertex. In standard position, the angle's vertex is placed at the origin, and the initial side is placed on the x-axis. The terminal side is the side that is allowed to move freely. The measure of the angle, \(m\angle ABC\), is found in between the two sides. Two angles are then co-terminal if their terminal sides match up. This is similar to being multiples of each other. The quadrant is also decided by the terminal angle.
Angle Measures
Angles can be measured in many different units. Degrees divide up the circle into \(360\degree\) (DEGREES), while each degree can be divided into \(60'\) (MINUTES), and each minute can be divided into \(60''\) (SECONDS). This system is called DMS. Another system is that of radians. This system has \(2\pi\) or \(\tau\) radians in a circle. They represent the arc length of the unit circle. Finally gradians are a system that divides the circle into \(400\ gons\) (GRADIANS). To convert between DEGREES and RADIANS, a scaling factor of \(\frac{180\degree}{\pi}\) or \(\frac{\pi}{180\degree}\) is used.