If the measure of angle ABE = 9x - 1 and the measure of angle DBC = 24x +14, find the measure of angle EBD. Can someone help me with this step-by-step? Thanks.

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Is ABC a straight line?  If so, then angle EBD = 180-24X-14-9x+1 = 180-33x-13.  You need to know something else about the given angles to find x and thus the angle.