Two angles are supplementary if the sum of their measures equals 180°. Given the measures of angle ACB and angle BCD as follows:
- \( m∠ACB = 4x° \)
- \( m∠BCD = (6x + 50)° \)
Set up the equation based on the definition of supplementary angles:
\[ m∠ACB + m∠BCD = 180° \]
Substituting the expressions for the angles:
\[ 4x + (6x + 50) = 180 \]
Simplify the equation:
\[ 4x + 6x + 50 = 180 \]
Combine like terms:
\[ 10x + 50 = 180 \]
Now, subtract 50 from both sides:
\[ 10x = 130 \]
Next, divide by 10:
\[ x = 13 \]
Now, substitute \( x \) back into the expression for \( m∠ACB \):
\[ m∠ACB = 4x = 4(13) = 52° \]
Thus, the measure of \( ∠ACB \) is:
\[ \boxed{52} \]
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