To find the measure of angle \( m∠BCD \), we start with the fact that angles \( ∠ACB \) and \( ∠BCD \) are supplementary. This means their measures add up to \( 180° \).
Given:
- \( m∠ACB = (x + 28)° \)
- \( m∠BCD = (x + 48)° \)
We can write the equation:
\[ m∠ACB + m∠BCD = 180° \]
Substituting the expressions for the angles, we get:
\[ (x + 28) + (x + 48) = 180 \]
Simplifying this:
\[ 2x + 76 = 180 \]
Now, we solve for \( x \):
\[ 2x = 180 - 76 \] \[ 2x = 104 \] \[ x = 52 \]
Now that we have the value of \( x \), we can find the measure of \( m∠BCD \):
\[ m∠BCD = x + 48 = 52 + 48 = 100° \]
Thus, \( m∠BCD \) is \( 100° \).
So the answer is:
100°