Question

$m\angle klm = m\angle lkn$ because they are alternate interior angles.
$m\angle lmk = m\angle mko$ because they are alternate interior angles.
$m\angle lkn + x^\circ + m\angle mko = 180^\circ$ because the three angles form a straight line.

so the value of $x$ must be 68

after moving the vertices, the new value of $x$ is $\square^\circ$
try

Explanation:

Step1: Identify alternate interior angles

$m\angle KLM = m\angle LKN = 42^\circ$, $m\angle LMK = m\angle MKO = 72^\circ$

Step2: Use straight angle sum property

The angles at point $K$ form a straight line, so $m\angle LKN + x + m\angle MKO = 180^\circ$

Step3: Substitute values and solve for $x$

$42 + x + 72 = 180$
$x = 180 - 42 - 72$

Answer:

$66$