Question

which angles are alternate interior angles?
image of lines and angles: two vertical lines (gi and df) and a transversal (jc) intersecting them at h and e respectively. points: g, i on one line; d, f on the other; j, h, e, c on the transversal. angles: ∠ghe, ∠dec, ∠deh, ∠feh, ∠ghj. options: ∠ghe and ∠dec; ∠ghe and ∠deh; ∠ghe and ∠feh; ∠ghe and ∠ghj

Explanation:

Step1: Recall Alternate Interior Angles Definition

Alternate interior angles are formed when a transversal crosses two parallel lines (or non - parallel lines, but the definition is about their position). They lie between the two lines (interior) and on opposite sides of the transversal.

Step2: Analyze Each Option

• For $\angle GHE$ and $\angle DEC$: $\angle DEC$ is not between the two lines (GI and DF), so this is not correct.
• For $\angle GHE$ and $\angle DEH$: $\angle GHE$ is at H (between GI and DF, on one side of transversal JC), $\angle DEH$ is at E (between GI and DF, on the other side of transversal JC). So they are alternate interior angles.
• For $\angle GHE$ and $\angle FEH$: $\angle FEH$ is not in the correct position relative to the transversal and the two lines.
• For $\angle GHE$ and $\angle GHJ$: $\angle GHJ$ is adjacent and not alternate interior.

Answer:

$\angle GHE$ and $\angle DEH$