To find the measure of angle \( \angle DBC \), we can use the fact that angles \( \angle ABD \) and \( \angle DBC \) are adjacent angles inside \( \angle ABC \).
Given:
- \( m\angle ABC = 160^\circ \)
- \( m\angle ABD = 92^\circ \)
We know that the sum of the measures of angles \( \angle ABD \) and \( \angle DBC \) should equal the measure of angle \( \angle ABC \):
\[ m\angle ABC = m\angle ABD + m\angle DBC \]
Substituting the known values into the equation:
\[ 160^\circ = 92^\circ + m\angle DBC \]
To find \( m\angle DBC \), we can rearrange the equation:
\[ m\angle DBC = 160^\circ - 92^\circ \]
Calculating the right-hand side:
\[ m\angle DBC = 68^\circ \]
Thus, the measure of angle \( \angle DBC \) is \( 68^\circ \).
The correct response is:
68°.