To find the measure of angle \( DBC \), we can use the fact that adjacent angles \( \angle ABD \) and \( \angle DBC \) together with \( \angle ABC \) form a straight line. This means that the sum of the measures of angles \( ABD \) and \( DBC \) is equal to the measure of angle \( ABC \).
The relationship can be expressed as: \[ m∠ABC = m∠ABD + m∠DBC \]
Given:
- \( m∠ABC = 160° \)
- \( m∠ABD = 92° \)
We can substitute the values into the equation: \[ 160° = 92° + m∠DBC \]
To find \( m∠DBC \), we can rearrange the equation: \[ m∠DBC = 160° - 92° \] \[ m∠DBC = 68° \]
Therefore, the measure of angle \( DBC \) is \( 68° \).
The correct response is: 68°