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I understood coterminal angles as angles that have the same terminal angle value. By this logic, why aren't 135 and 315 coterminal? They both have a terminal angle of 45.

Is my interpretation of coterminal angles wrong?

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How do you define "terminal angle" to begin with? One's obtuse, and the other's a reflex angle... –  J. M. Apr 27 '12 at 3:30
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Both angles have to start at the same place and end at the same place. If you "start" your 135 degree angle on the positive $x$-axis, it finishes in the second quadrant; but the 315 degree angle started on the positive $x$-axis "ends" in the fourth quadrant. So how can you say they are "coterminal", if they don't end in the same place? –  Arturo Magidin Apr 27 '12 at 3:40
    
Two angles are coterminal if and only if their difference is a mutiple of $360^\circ$. –  André Nicolas Apr 27 '12 at 5:19

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Two angles a are coterminal if their difference is a multiple of 360°. What that means is that two angles are coterminal when they start and end in the same place. Examples of Coterminal angles are
180° and − 180°
170° and − 190°
100° and − 260°
360° and 720 °
360° and − 360°

Another way of explaining is that Coterminal angles are angles in standard position (angles with the initial side on the positive x-axis) that have a common terminal side. For example 30°, –330° and 390° are all coterminal.(look below).Here –330° is the negative coterminal angle of 30° and 390°is positive coterminal angle of 30°.

Graphical example

So according to your question 135 and 315 cannot be coterminal as they do not lie on one another.hope that helps

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srry i meant their difference is 360(il make that edit).thus $30-(-330)=360$ and $390-30=360$. 390 and -330 are not coterminal angles of each other so u cant subtract them to get 360. hope you understand what i mean –  Ashu Apr 27 '12 at 14:49
    
Okay, that makes more sense... –  Arturo Magidin Apr 27 '12 at 14:58

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