Two angles are supplementary if the sum of their measures equals 180 degrees. Given the measures of the angles, we have:
- \( m \angle ABC = 135 \) degrees
- \( m \angle CBD = 9x \) degrees
Since these angles are supplementary, we can set up the following equation:
\[ m \angle ABC + m \angle CBD = 180 \]
Substituting the given values, we get:
\[ 135 + 9x = 180 \]
This is the equation you need to solve for \( x \).