Question

in the figure below, which set of angles are not congruent? select the correct answer ∠e and ∠c ∠d and ∠l ∠g and ∠c ∠g and ∠h

Explanation:

Step1: Recall angle - congruence rules

When two parallel lines are cut by a transversal, corresponding angles are congruent, alternate - interior angles are congruent, and vertical angles are congruent.

Step2: Analyze each option

• $\angle e$ and $\angle c$: $\angle e$ and $\angle c$ are vertical angles. Vertical angles are always congruent.
• $\angle d$ and $\angle l$: $\angle d$ and $\angle l$ are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are congruent.
• $\angle g$ and $\angle c$: $\angle g$ and $\angle c$ are neither vertical angles, corresponding angles, nor alternate - interior angles. They are not congruent in general.
• $\angle g$ and $\angle h$: $\angle g$ and $\angle h$ are vertical angles. Vertical angles are always congruent.

Answer:

$\angle g$ and $\angle c$