Supplementary angles are two angles that add up to 180 degrees. Given that \( m∠ABC = 15° \) and \( m∠CBD = x° \), we can set up the equation:
\[ m∠ABC + m∠CBD = 180° \]
Substituting the known value:
\[ 15° + x° = 180° \]
To find \( x° \), we can subtract 15° from both sides:
\[ x° = 180° - 15° \] \[ x° = 165° \]
Thus, the value of \( m∠CBD \) is 165°.