fh and ik are parallel lines. select all the pairs of alternate interior angles. ∠hgj and ∠ijg ∠kjg and ∠fgj ∠hge and ∠ijg ∠fgj and ∠hge

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Accepted Answer

# 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 $\angle HGJ$ and $\angle IJG$:
  - Lines $FH\parallel IK$ and transversal $LJ$.
  - $\angle HGJ$ and $\angle IJG$ are between $FH$ and $IK$ and on opposite sides of $LJ$.
- For $\angle KJG$ and $\angle FGJ$:
  - Lines $FH\parallel IK$ and transversal $LJ$.
  - $\angle KJG$ and $\angle FGJ$ are between $FH$ and $IK$ and on opposite sides of $LJ$.
- For $\angle HGE$ and $\angle IJG$:
  - Lines $FH\parallel IK$ and transversal $LJ$.
  - $\angle HGE$ and $\angle IJG$ are not between the two parallel lines ( $\angle HGE$ is an exterior - related angle in terms of the parallel lines $FH$ and $IK$ in the wrong position).
- For $\angle FGJ$ and $\angle HGE$:
  - Lines $FH\parallel IK$ and transversal $LJ$.
  - $\angle FGJ$ and $\angle HGE$ are not alternate interior angles (they are not in the correct "between - the - parallel - lines and opposite - sides - of - transversal" configuration).

# Answer:
$\angle HGJ$ and $\angle IJG$, $\angle KJG$ and $\angle FGJ$

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Question

Explanation:

Step1: Recall the definition of alternate interior angles

Step2: Analyze each pair

Answer: