Supplementary angles are two angles whose measures add up to 180 degrees. Given that \( m\angle ABC = 105^\circ \) and \( m\angle CBD = (3x - 24)^\circ \), you can set up the equation as follows:
\[ 105 + (3x - 24) = 180 \]
Now, to simplify it:
- Combine like terms: \[ 105 - 24 + 3x = 180 \] \[ 81 + 3x = 180 \]
So the equation to solve for \( x \) is: \[ 81 + 3x = 180 \]
From here, you can isolate \( x \) by subtracting 81 from both sides and then dividing by 3.