To find the equation for the measures of the two supplementary angles, we recall that supplementary angles sum to 180°. Given:
- \( m\angle ABC = 105° \)
- \( m\angle CBD = (3x - 24)° \)
Since these angles are supplementary, we can set up the following equation:
\[ m\angle ABC + m\angle CBD = 180° \]
Substituting the values we have:
\[ 105° + (3x - 24)° = 180° \]
To write this in the form you're asking for:
\[ (3x - 24)° + 105° = 180° \]
So, the complete equation to solve for \( x \) is:
\[ (3x - 24) + 105 = 180 \]
You can simplify it further if needed but that's the primary equation.