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Since ∠ABC is 160° and ∠ABD is 92°, the measure of ∠DBC can be found by subtracting the measure of ∠ABD from ∠ABC:
∠DBC = ∠ABC - ∠ABD
∠DBC = 160° - 92°
∠DBC = 68°
Therefore, the angle measure of DBC is 68°.