\(KLP\) and \(PLM\) form a linear pair, so:
\(KLP + PLM = 180\)
\(3x + PLM = 180\)
\(PLM = 180-3x\)
Same with \(PMN\) and \(PML\), so:
\(PMN + PML = 180\)
\((2x+72) + PML = 180\)
\(PML = 108-2x\)
Since \(PLM\), \(PML\), and \(LPM\) are the angles of the same triangle, their sums must be equal to \(180\). So:
\(PML + PLM + LPM = 180\)
\((108-2x) + (180-3x) + (x) = 180\)
\(288-4x=180\)
\(-4x = -108\)
\(x = 27\)
