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Angles are fundamental elements in geometry and trigonometry, and they describe the amount of rotation between two rays that meet at a common endpoint, known as the vertex. Angles are often measured in degrees, and a full rotation around a point is equivalent to 360 degrees. This unit of measurement allows us to define angles varying from very tiny rotations to complete circles.

When studying angles, it's essential to understand how they function in cycles, meaning that once you exceed 360 degrees, you've essentially made a complete circle and end up back at a point that might be called a coterminal position. This is important when we discuss coterminal angles, which may appear different numerically but occupy the same position or orientation on a circular path.

Positive angles are angles that are measured in a counter-clockwise direction starting from the positive x-axis. This direction follows the traditional mathematic standard way of describing angular direction. In math, when you continue to add multiples of 360 degrees to an angle, you continue to move in the counter-clockwise direction around a circle.

For instance, if you start at an angle of 140 degrees and add 360 degrees, you end up at 500 degrees. Numerically, this may seem large, but geometrically, this angle ends up pointing in the same direction as 140 degrees. This is because 500 degrees is a coterminal angle with 140 degrees. The concept of addition of 360 degrees can be repeated, allowing for positive angles to continue infinitely.

Negative angles are angles measured in a clockwise direction. This is the opposite of the standard positive direction and is often slightly more confusing as it involves moving backwards, in a sense, in degrees. Negative angles are useful in many mathematical contexts, because they provide a way to indicate direction distinctively.

When you take a given angle, such as 140 degrees, and subtract 360 degrees, you move in a clockwise direction, and obtain a negative angle. Here, subtraction of 360 degrees from 140 degrees results in -220 degrees, which is a negative coterminal angle of 140 degrees. Again, this angle is beneficial in understanding rotational motion or when working with coordinate systems, ensuring that the same position can be represented in an alternate fashion.