Supplementary angles are two angles whose measures add up to 180 degrees.
Given:
- \( m∠ABC = 15° \)
- \( m∠CBD = x° \)
Since these angles are supplementary, we have:
\[ m∠ABC + m∠CBD = 180° \]
Substituting the value of \( m∠ABC \):
\[ 15° + x° = 180° \]
Now, to find \( x \):
\[ x = 180° - 15° \]
\[ x = 165° \]
Therefore, the value of \( m∠CBD \) is 165°.