Question

name two pairs of congruent angles in the figure. justify the answer. select all that apply. a. ∠lip and ∠kil according to the linear pair theorem b. ∠kil and ∠mip according to the congruent complements theorem c. ∠kim and ∠lip according to the congruent complements theorem d. ∠kim and ∠mip according to the linear pair theorem

Explanation:

Step1: Recall Linear - Pair Theorem

The Linear - Pair Theorem states that if two angles form a linear pair, they are supplementary (sum to 180°) but not necessarily congruent.

Step2: Recall Congruent Complements Theorem

The Congruent Complements Theorem states that if two angles are complements of the same angle, then they are congruent.

Step3: Analyze Option A

∠LIP and ∠KIL do not form a linear - pair. A linear pair consists of two adjacent angles whose non - common sides are opposite rays. So, option A is incorrect.

Step4: Analyze Option B

If ∠KIL and ∠MIP are both complements of ∠LIM, then by the Congruent Complements Theorem, ∠KIL≅∠MIP. This option is correct.

Step5: Analyze Option C

If ∠KIM and ∠LIP are both complements of ∠LIM, then by the Congruent Complements Theorem, ∠KIM≅∠LIP. This option is correct.

Step6: Analyze Option D

∠KIM and ∠MIP do not form a linear pair. A linear pair has adjacent angles with non - common sides as opposite rays. So, option D is incorrect.

Answer:

B. ∠KIL and ∠MIP according to the Congruent Complements Theorem
C. ∠KIM and ∠LIP according to the Congruent Complements Theorem