To find the equation to solve for \( x \) given that the angles are supplementary, we start by recalling that two supplementary angles add up to \( 180^\circ \).
Given:
- \( m∠ABC = 135^\circ \)
- \( m∠CBD = 9x^\circ \)
Since these angles are supplementary, we can set up the equation:
\[ m∠ABC + m∠CBD = 180^\circ \]
Substituting the measures into the equation gives us:
\[ 135^\circ + 9x^\circ = 180^\circ \]
Therefore, the correct equation to solve for \( x \) is:
\[ 9x^\circ + 135^\circ = 180^\circ \]
So, the appropriate response is:
9x°+135°=180°.