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Find the value of x.

 

 Oct 4, 2020
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\(KLP\) 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:

\(PML + PLM + LPM = 180\) 

\((108-2x) + (180-3x) + (x) = 180\)

\(288-4x=180\)

\(-4x = -108\)

\(x = 27\)

 

surprisesurprise

 Oct 4, 2020

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