Question

look at this diagram:
diagram of lines km, np (parallel) and transversal qj intersecting them at o and l, with points n, p on np; k, m on km; q, j on qj
if \\(\overleftrightarrow{km}\\) and \\(\overleftrightarrow{np}\\) are parallel lines and \\(m\angle pol = 130^\circ\\), what is \\(m\angle mlo\\)?
blank box for answer\\(^\circ\\)
submit

Explanation:

Step1: Identify supplementary angle

$\angle POL$ and $\angle NOQ$ are vertical angles, so $m\angle NOQ = 130^\circ$. $\angle NOQ$ and $\angle QOP$ are supplementary:
$m\angle QOP = 180^\circ - 130^\circ = 50^\circ$

Step2: Use parallel line alternate interior angles

Since $\overleftrightarrow{KM} \parallel \overleftrightarrow{NP}$, $\angle QOP$ and $\angle MLO$ are alternate interior angles, so they are congruent.
$m\angle MLO = m\angle QOP$

Answer:

$50^\circ$