Since angles ∠ACB and ∠BCD are supplementary, their measures add up to 180 degrees. We can set up the equation based on the given measures:
\[ \angle ACB + \angle BCD = 180^\circ \]
Substituting the expressions for the angles,
\[ (x + 28) + (x + 48) = 180 \]
Now, combine like terms:
\[ 2x + 76 = 180 \]
Next, we can solve for \( x \):
\[ 2x = 180 - 76 \] \[ 2x = 104 \] \[ x = 52 \]
Now we need to find m∠BCD:
\[ m∠BCD = x + 48 \] \[ m∠BCD = 52 + 48 = 100 \]
Therefore, the measure of angle BCD is:
\[ \boxed{100^\circ} \]