Two angles are supplementary when their measures add up to 180°. Given the angles:
\[ m∠ACB = 4x° \quad \text{and} \quad m∠BCD = (6x + 50)° \]
Since these two angles are supplementary, we have:
\[ m∠ACB + m∠BCD = 180° \]
Substituting the expressions for the angles:
\[ 4x + (6x + 50) = 180 \]
Now, combine like terms:
\[ 4x + 6x + 50 = 180 \]
Which simplifies to:
\[ 10x + 50 = 180 \]
Next, subtract 50 from both sides:
\[ 10x = 130 \]
Now, divide by 10:
\[ x = 13 \]
Now that we have the value of \( x \), we can find \( m∠ACB \):
\[ m∠ACB = 4x = 4(13) = 52° \]
Thus, the measure of \( ∠ACB \) is:
\[ \boxed{52°} \]