Question

the figure shows a transversal that intersects two parallel lines. none of the angles are right angles. decide whether each pair of angles is congruent or not congruent. angles congruent or not congruent ∠2 and ∠5 not congruent ∠2 and ∠7 congruent ∠4 and ∠8 congruent ∠3 and ∠8?

Explanation:

Step1: Recall the properties of parallel lines and transversals

When a transversal intersects two parallel lines, corresponding angles are congruent, alternate - interior angles are congruent, alternate - exterior angles are congruent, and consecutive - interior angles are supplementary.

Step2: Analyze the relationship between \(\angle3\) and \(\angle8\)

We know that \(\angle3\) and \(\angle4\) are supplementary (\(\angle3+\angle4 = 180^{\circ}\) since they form a linear pair). Also, \(\angle4\) and \(\angle8\) are congruent (corresponding angles as the lines are parallel). Let \(\angle4=\angle8 = x\). Then \(\angle3=180 - x\). Since \(x
eq90^{\circ}\) (given no right - angles), \(\angle3
eq\angle8\)

Answer:

not congruent