Question

look at this diagram:
diagram with lines and points
if \\( \overleftrightarrow{fh} \\) and \\( \overleftrightarrow{ik} \\) are parallel lines and \\( m\angle hgj = 51^\circ \\), what is \\( m\angle kjg \\)?
blank box for answer\\( ^\circ \\)

Explanation:

Step1: Identify alternate interior angles

Since $\overleftrightarrow{FH} \parallel \overleftrightarrow{IK}$ and transversal $\overleftrightarrow{LE}$ intersects them, $\angle HGJ$ and $\angle KJG$ are alternate interior angles.

Step2: Apply alternate interior angles theorem

Alternate interior angles formed by parallel lines are congruent, so $m\angle KJG = m\angle HGJ$.
<Expression>
$m\angle KJG = 51^\circ$
</Expression>

Answer:

$51^\circ$