To find the measure of angle \( \angle DBC \), we can use the fact that the sum of the adjacent angles \( \angle ABD \) and \( \angle DBC \) is equal to the measure of angle \( \angle ABC \).
Given:
- \( m\angle ABC = 160^\circ \)
- \( m\angle ABD = 92^\circ \)
We can set up the equation:
\[ m\angle ABC = m\angle ABD + m\angle DBC \]
Substituting the known values:
\[ 160^\circ = 92^\circ + m\angle DBC \]
To find \( m\angle DBC \):
\[ m\angle DBC = 160^\circ - 92^\circ = 68^\circ \]
Therefore, the measure of angle \( DBC \) is \( 68^\circ \).
The correct response is: 68°