Two angles are supplementary if the sum of their measures is 180 degrees. Given:
- \( m\angle ACB = x \)
- \( m\angle BCD = 26^\circ \)
Since these angles are supplementary, we can set up the equation:
\[ x + 26 = 180 \]
To find \( x \), subtract 26 from both sides:
\[ x = 180 - 26 \] \[ x = 154 \]
So, the measure of \( \angle ACB \) is \( 154^\circ \).
Next, to find \( m\angle ACD \), we note that \( \angle ACD \) is formed by \( \angle ACB \) and \( \angle BCD \):
\[ m\angle ACD = m\angle ACB + m\angle BCD = 154 + 26 \] \[ m\angle ACD = 180^\circ \]
Thus, the measure of \( \angle ACD \) is:
\[ m\angle ACD = 180^\circ \]
In summary:
- \( m\angle ACB = 154^\circ \)
- \( m\angle ACD = 180^\circ \)