Question 596366
In trigonometry, angles are usually shown in what is called standard position, with a side, taken as the initial side, coinciding with the positive x-axis.
The other side is called the terminal side, and the angle is seen as a turn or sweep from the initial side to the terminal side.
Counter-clockwise angles (turns) are considered to have a positive measure, while clockwise turns have negative measures.
The measure of one whole counter-clockwise turn would be {{{360^o}}}.
More than one turn is allowed, so angles can have any measure, from -infinity to +infinity.
Two counterclockwise turns would be a {{{720^o}}} angle.
The sides of angles differing by one or more turns (like {{{360^o}}} and {{{720^o}}} angles) coincide.
Those angles are said to be co-terminal to each other.
{{{drawing(300,300,-1.4,1.4,-1.4,1.4,
circle(0,0,1),
arrow(0,0,1.4,0),arrow(0,0,-1.4,0),
arrow(0,0,0,1.4),arrow(0,0,0,-1.4),
locate(0.1,1.4,y),locate(1.35,0,x),
red(arrow(0,0,1.2,0)),red(arrow(0,0,0.85,-0.85)),
locate(-.1,0.15,O),locate(0.9,0.15,A),locate(0.7,-0.74,B)
)}}} The {{{1/8}}}-turn clockwise, acute angle AOB has a measure of {{{-45^o}}}.
The other (counter-clockwise, {{{7/8}}}-turn) angle AOB has a measure of {{{360^o-45^o=315^o}}}.
It is one of an infinite number of angles coterminal with the {{{-45^o}}} angle AOB, but the only one between {{{0^o}}} and {{{360^o}}} is the {{{7/8}}}-turn counter-clockwise AOB measuring {{{highlight(315^o)}}}.