Two angles are supplementary if the sum of their measures is 180 degrees. In this case, we have:
\( m∠ABC = 15° \) \( m∠CBD = x° \)
Since these angles are supplementary, we can set up the equation:
\[ m∠ABC + m∠CBD = 180° \]
Substituting the known value:
\[ 15° + x° = 180° \]
To find \( x \), we subtract 15° from both sides:
\[ x° = 180° - 15° \] \[ x° = 165° \]
Therefore, \( m∠CBD = 165° \).
The correct response is: 165 degrees.