THe measure of ∠ABC is 102°, find the measure of ∠DBC.

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Depending on the diagram for the problem, there could be different answers to this question. I am going to assume that A, B and D are all on the same line with B between A & D. C is therefore on a line that intersects this line at point B.

Angle ABC is 102 (given) and the angle DBC forms a linear pair with the angle. This means that the two angles together form a straight line and are supplementary. Thus, 102 + angle DBC - 180 and therefore, angle DBC = 78 degrees.

ABC+DBC=180

102+DBC=180

102+DBC-102=180-102

DBC=78 degree

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