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