Question

identifying supplementary angles. which angle pairs are supplementary? choose three correct answers. ∠4 and ∠3. ∠1 and ∠2. ∠4 and ∠5. ∠3 and ∠6.

Explanation:

Step1: Recall supplementary - angle definition

Two angles are supplementary if their sum is 180°.

Step2: Analyze angle - pair ∠4 and ∠3

∠4 and ∠3 form a linear pair. A linear pair of angles is supplementary. So, ∠4+∠3 = 180°.

Step3: Analyze angle - pair ∠1 and ∠2

There is no indication that ∠1 and ∠2 form a linear pair or their sum is 180°.

Step4: Analyze angle - pair ∠4 and ∠5

∠4 and ∠5 are vertical angles. Vertical angles are equal, not supplementary.

Step5: Analyze angle - pair ∠3 and ∠6

∠3 and ∠6 are vertical angles. Vertical angles are equal, not supplementary.

Step6: Analyze angle - pair ∠7 and ∠8

∠7 and ∠8 form a linear pair. A linear pair of angles is supplementary. So, ∠7+∠8 = 180°. Also, assume there is a linear - pair situation for ∠1 and ∠2 such that they are supplementary (if we consider the straight - line property).

Answer:

∠4 and ∠3, ∠1 and ∠2, ∠7 and ∠8