To find the measure of angle DBC, we can use the fact that adjacent angles within a larger angle should sum up to the measure of the larger angle.
Given:
- m∠ABC = 160°
- m∠ABD = 92°
Since ∠ABD and ∠DBC are adjacent angles inside ∠ABC, you can set up the equation:
m∠ABC = m∠ABD + m∠DBC
Plugging in the values we have:
160° = 92° + m∠DBC
Now, solve for m∠DBC:
m∠DBC = 160° - 92° m∠DBC = 68°
So, the measure of angle DBC is 68°.