Question

look at this diagram:
if \\( \overleftrightarrow { k m } \\) and \\( \overleftrightarrow { n p } \\) are parallel lines and \\( m \angle k l j = 136 ^ { \circ } \\), what is \\( m \angle m l j \\)?

Explanation:

Step1: Identify angle relationship

∠KLJ and ∠MLJ are supplementary (form a linear pair) as they lie on a straight line (KM is a straight line, and LJ is a transversal). So, \( m\angle KLJ + m\angle MLJ = 180^\circ \).

Step2: Solve for \( m\angle MLJ \)

Given \( m\angle KLJ = 136^\circ \), substitute into the equation:
\( 136^\circ + m\angle MLJ = 180^\circ \)
Subtract \( 136^\circ \) from both sides:
\( m\angle MLJ = 180^\circ - 136^\circ = 44^\circ \).

Answer:

\( 44 \)