Supplementary angles are two angles whose measures add up to 180 degrees. In this case, you have:
- \( m∠ABC = 15° \)
- \( m∠CBD = x° \)
Since these angles are supplementary, you can set up the equation:
\[ m∠ABC + m∠CBD = 180° \]
Substituting the known value:
\[ 15° + x° = 180° \]
Now, solve for \( x \):
\[ x° = 180° - 15° \] \[ x° = 165° \]
Therefore, the value of \( m∠CBD \) is 165 degrees.