Question

look at this diagram:

diagram of parallel lines ln and ik, and transversal oh intersecting them at m and j respectively, with points l, n on ln; i, k on ik; o, m, j, h on oh

if \\( \overleftrightarrow{ik} \\) and \\( \overleftrightarrow{ln} \\) are parallel lines and \\( m\angle lmo = 59^\circ \\), what is \\( m\angle kjm \\)?

\\( \square^\circ \\)

Explanation:

Step1: Identify vertical angles

$\angle LMO = \angle NMJ = 59^\circ$

Step2: Use parallel line property

$\angle NMJ$ and $\angle KJM$ are same-side interior angles, so they are supplementary.
$\angle KJM = 180^\circ - \angle NMJ$

Step3: Calculate the angle

$\angle KJM = 180^\circ - 59^\circ = 121^\circ$

Answer:

$121$