Question

$overleftrightarrow{hj}$ and $overleftrightarrow{km}$ are parallel lines.
which angles are alternate interior angles?
$\angle mli$ and $\angle hil$ $\angle mli$ and $\angle hig$
$\angle mli$ and $\angle jil$ $\angle mli$ and $\angle kli$

Explanation:

Step1: Recall the definition of alternate interior angles

Alternate interior angles are formed when a transversal crosses two parallel lines. They lie between the two parallel lines and on opposite sides of the transversal.

Step2: Analyze each pair

• For \(\angle MLI\) and \(\angle HIL\): They are same - side interior angles (sum to \(180^{\circ}\) if lines are parallel), not alternate interior.
• For \(\angle MLI\) and \(\angle HIG\): \(\angle HIG\) is an exterior - related angle. These are not alternate interior.
• For \(\angle MLI\) and \(\angle JIL\): Since \(\overleftrightarrow{KM}\parallel\overleftrightarrow{HJ}\) and \(NG\) is the transversal. \(\angle MLI\) and \(\angle JIL\) lie between the parallel lines \(KM\) and \(HJ\) and on opposite sides of the transversal \(NG\).
• For \(\angle MLI\) and \(\angle KLI\): They are adjacent angles (form a linear pair), not alternate interior.

Answer:

\(\angle MLI\) and \(\angle JIL\)