The two angles are supplementary, which means that their measures add up to 180 degrees. Given that:
- \( m∠ACB = x \)°
- \( m∠BCD = 26 \)°
We can write the equation:
\[ x + 26 = 180 \]
To find the measure of \( m∠ACB \), we can subtract 26 from both sides:
\[ x = 180 - 26 \] \[ x = 154 \]
Therefore, the measure of \( m∠ACB \) is:
\[ \boxed{154}° \]