Question

for items 2 - 3, use the figure shown. select all the angles that are supplementary to ∠1. a ∠3 b ∠4 c ∠5 d ∠6 e ∠7 f ∠8

Explanation:

Step1: Recall supplementary - angle definition

Two angles are supplementary if their sum is 180°. Adjacent angles on a straight - line are supplementary.

Step2: Identify adjacent angles to ∠1

∠1 and ∠2 are adjacent and form a straight - line, so ∠1+∠2 = 180°. Also, ∠1 and ∠4 are adjacent and form a straight - line, so ∠1+∠4 = 180°.

Step3: Consider vertical - angle and supplementary relationships

∠1 and ∠5 are vertical angles to ∠4 and ∠2 respectively. Since ∠4 and ∠2 are supplementary to ∠1, and vertical angles are equal, ∠5 is also supplementary to ∠1. Also, ∠1 and ∠8 are vertical angles to ∠2 and ∠4 respectively, so ∠8 is supplementary to ∠1.

Answer:

B. ∠2, C. ∠4, E. ∠5, F. ∠8