To find the angle measure of ∠DBC, we can use the fact that adjacent angles, such as ∠ABD and ∠DBC, add up to the measure of the larger angle ∠ABC.
Given:
- m∠ABC = 160°
- m∠ABD = 92°
We can use the equation: m∠ABC = m∠ABD + m∠DBC
Substituting the known values: 160° = 92° + m∠DBC
Now, solve for m∠DBC: m∠DBC = 160° - 92° m∠DBC = 68°
Therefore, the measure of angle DBC is 68°.