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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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1 Answer

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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°.

_{(source: hotmath.com)}

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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