geometry

Question

+1

399

1

Find the value of x.

Guest Oct 4, 2020

Guest · Answer 1 · 2020-10-04T01:39:37

$KLP$ 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:

$PML + PLM + LPM = 180$

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

$288-4x=180$

$-4x = -108$

$x = 27$