Complementary angles are two angles whose measures add up to 90 degrees. Given that angle JKL is 34 degrees and that it is complementary to angle GHI, we can set up the equation:
\[ \text{angle JKL} + \text{angle GHI} = 90^\circ \]
Substituting the value we know:
\[ 34^\circ + x = 90^\circ \]
To find x (which represents angle GHI), we subtract 34 degrees from both sides:
\[ x = 90^\circ - 34^\circ \] \[ x = 56^\circ \]
Thus, the measure of angle GHI is 56 degrees.