Question 1199545
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You seem to have some misconceptions about coterminal angles.<br>
Given the measure of an angle, there are an infinite number of coterminal angles -- found by adding or subtracting any multiple of 360 degrees to the measure of the given angle.<br>
So it is incorrect (or, at least, nonstandard) terminology to talk about "THE" coterminal angle of a given angle.<br>
With your given angle of -240 degrees, ONE coterminal angle is -240+360 = 120 degrees.  But other coterminal angles are -240-360 = -600 degrees, or -240-720 = -960 degrees, or -240+1080 = 840 degrees, or an infinite number of others.<br>
In many instances, it makes sense to view an angle between 0 and 360 degrees as the "primary" coterminal angle, so in your case the "primary" coterminal angle is 120 degrees.<br>
I have never seen a reference that talks about the "lowest negative coterminal angle".  Apparently the reference you are using calls the coterminal angle between 0 and -360 degrees the lowest negative coterminal angle; since the given angle -240 degrees is already in that range, it is the lowest negative coterminal angle.<br>
I hope that helps....<br>