An angle is the result of two rays meeting at a vertex.

Angles are typically measured in degrees or radians.

The measure of an angle is represented as 𝜭 (theta) or any other variable.

Different sizes of angles have names:

0-degree angle
acute angle
right angle (90)
obtuse angle
straight angle (180)
360-degree angle

Two angles that sum to 90° or pi/2 are called complementary angles

Two angles that sum to 180° or pi are called supplementary angles

Standard position

If you line angles up on a cartesian coordinate system you can measure from the initial side to the terminal side and have positive angles that rotate counterclockwise and negative angles that rotate clockwise.

Remember that the cartesian system is numbered counterclockwise, top right 1, top left 2, etc…

Two angles are coterminal if their terminal sides overlap. (so an angle +- 2pi)

Converting between degrees, radians, and DMS(degrees, minutes, seconds)

One complete circle is 360° or 2pi radians.

To convert from degrees to radians, multiply by pi/180

radians = degrees(pi/180)

so,

degrees = radians(180/pi)

To find minutes and seconds, multiply any decimal of a degree by 60

72.75° = 72°(.75 * 60)' = 72°45'