To solve for \( x \) given that angles \( \angle ABC \) and \( \angle CBD \) are supplementary, we can set up the equation based on the definition of supplementary angles (the sum of the angles equals 180 degrees).
We know that: \[ \angle ABC = 3x + 25 \] \[ \angle CBD = 32 \]
Since these two angles are supplementary, we can write the equation as follows:
\[ (3x + 25) + 32 = 180 \]
Now, let's simplify the equation: \[ 3x + 25 + 32 = 180 \]
Combine the constants: \[ 3x + 57 = 180 \]
Now, in the format you asked for, we can express this equation as: \[ 3x + 57 = 180 \]
To put it in the exact form you requested: \[ 3x + 57 = 180 \]