Question

in the figure below, $\triangle klm$ is drawn. the line $\overleftrightarrow{nko}$ is drawn such that $\overleftrightarrow{nko} \parallel \overline{lm}$.

$\text{m}\angle klm = \underline{\quad}$ because they are $\underline{\quad}$

Explanation:

Step1: Find $\angle MKL$ in $\triangle KLM$

Sum of angles in a triangle is $180^\circ$.
$\angle MKL = 180^\circ - 83^\circ - 29^\circ = 68^\circ$

Step2: Relate $\angle MKL$ to $x$

$\overleftrightarrow{NKO} \parallel \overline{LM}$, so $\angle LKN = \angle KLM = 29^\circ$ (alternate interior angles). Then $x = 180^\circ - \angle MKL - \angle LKN$
$x = 180^\circ - 68^\circ - 29^\circ = 83^\circ$
(Alternatively, use corresponding angles: $\angle OKM = \angle KML = 83^\circ$, and $\angle OKM = x$ as vertical angles)

Answer:

$m\angle KLM = 29^\circ$ because they are alternate interior angles
The value of $x$ is $83^\circ$