To solve for \( x \) in the case of supplementary angles, we know that the sum of two supplementary angles is \( 180^\circ \).
Given:
- \( m\angle ABC = 135^\circ \)
- \( m\angle CBD = 9x^\circ \)
The equation to represent the sum of these two angles being supplementary is:
\[ m\angle ABC + m\angle CBD = 180^\circ \]
Substituting in the measures we have:
\[ 135^\circ + 9x^\circ = 180^\circ \]
To isolate \( 9x \), you would rearrange it as follows:
\[ 9x^\circ + 135^\circ = 180^\circ \]
Therefore, the correct response is:
9x° + 135° = 180°