Since angles ∠ACB and ∠BCD are supplementary, their measures add up to 180°:
\[ m∠ACB + m∠BCD = 180° \]
Given the measures of the angles:
\[ (x + 28) + (x + 48) = 180 \]
Now, combine like terms:
\[ 2x + 76 = 180 \]
Next, solve for \(x\) by subtracting 76 from both sides:
\[ 2x = 180 - 76 \] \[ 2x = 104 \]
Now, divide by 2:
\[ x = 52 \]
Now we can find the measure of ∠BCD:
\[ m∠BCD = x + 48 \] \[ m∠BCD = 52 + 48 = 100° \]
Therefore, the measure of ∠BCD is 100°.