Two angles are supplementary if the sum of their measures is 180 degrees.
In this case, you have one angle measuring 60 degrees and the other angle is \( X \).
To find \( X \), you can set up the equation:
\[ 60 + X = 180 \]
Now, subtract 60 from both sides:
\[ X = 180 - 60 \]
\[ X = 120 \]
So, the measure of \( X \) is 120 degrees.
Thus, \( X = 120 \).