To solve for \( x \) given that angles \( m∠ABC \) and \( m∠CBD \) are supplementary, we use the definition of supplementary angles. Supplementary angles sum up to \( 180^\circ \).
We know that:
- \( m∠ABC = 105^\circ \)
- \( m∠CBD = (3x - 24)^\circ \)
The equation representing their supplementary relationship is: \[ m∠ABC + m∠CBD = 180^\circ \]
Substituting the angles into the equation gives: \[ 105^\circ + (3x - 24)^\circ = 180^\circ \]
This is the equation you need to solve for \( x \).
So the final form of the equation is: \[ 105 + (3x - 24) = 180 \]