Question

which angles are congruent to ∠7? why are they congruent to ∠7? select two that apply. a. ∠8 because linear pairs are congruent b. ∠6 because vertical angles are congruent c. ∠4 because alternate interior angles are congruent d. ∠3 because corresponding angles are congruent

Explanation:

Step1: Recall angle - congruence rules

Vertical angles are congruent, alternate - interior angles are congruent when two parallel lines are cut by a transversal, and corresponding angles are congruent when two parallel lines are cut by a transversal. Linear pairs are supplementary (sum to 180°), not congruent.

Step2: Analyze each option

• Option A: Linear pairs are supplementary, not congruent. So, ∠8 is not congruent to ∠7 because linear pairs are congruent is a wrong statement.
• Option B: If ∠7 and ∠6 are vertical angles (formed by the intersection of two lines), then by the vertical - angle theorem, vertical angles are congruent. So, ∠6 is congruent to ∠7.
• Option C: There is no information indicating that the lines are parallel. So, we cannot assume that alternate - interior angles are congruent.
• Option D: If the lines are parallel and ∠7 and ∠3 are corresponding angles (in the same relative position with respect to the parallel lines and the transversal), then by the corresponding - angle postulate, corresponding angles are congruent.

Answer:

B. ∠6 because vertical angles are congruent
D. ∠3 because corresponding angles are congruent