When understanding movement, techniques, and positioning, these angles become very important.

Facing straight ahead, in this four-cornered room, movement to the left and right would be 90-degree turns. Technically, to turn all the way around to face the back wall would be a 180-degree turn, which is two 90-degree turns. In common and simple usage, while training, speaking of a 90 (a direction that is 90 degrees from your position) is considered a direction straight in front, to the left or right, or in back of you.

However, when speaking of movement, one can speak of 45-degree turns (a movement towards the corner), 90-degree turns (movement to either side), 180-degree turns (turning around to face the opposite direction), or 360-degree turns (making a complete spin around to end up facing where you started). As might be expected, these movements can accompany footwork, kicks, striking, throws, and locks.

It should be noted that I've simplified these mathematical degrees to make it easier to understand in terms of martial arts training. It is simply easier to refer to the 90-degree angles as straight shots ahead, to the sides, and in back of you; while the 45-degree angles are simpler as references to directions towards the corners.

Mathematically, however, these angles are based on the circle, which is measured as having 360 degrees. Straight ahead would be zero; straight to the right (if moving clock-wise) is the 90-degree angle; the right triangle is like a big wedge out of the circle, like you sliced a big hunk of pie; the 45-degree angle is halfway between zero and 90 degrees; half of 90 is 45, 45 two times is 90; as you continue the circle (from 90 degrees), another 45 degrees would be 135, which would be a back corner; go another 45 degrees and you have 180 degrees, which is the back wall, an about face; add another 45 degrees and you have 225 degrees and you'd face the other back corner (southwest). Add yet another 45 degrees and you are at 270 degrees, facing straight towards the left side from where you started; another 45 degrees and you have 315 degrees towards the front corner (from where you started), northwest; tack on another 45 degrees and you have 360 degrees, a full circle, facing where you started.