Question

in this figure, line x is parallel to line y and m∠1 = 64°. what is the measure of ∠8? 1. enter question text

Explanation:

Step1: Identify angle relationship

∠1 and ∠4 are adjacent supplementary angles? Wait, no, line x and y are parallel, and the transversal. Wait, ∠1 and ∠5? Wait, no, looking at the diagram, ∠1 and ∠2 are supplementary? Wait, no, ∠1 and ∠4: Wait, actually, ∠1 and ∠4? Wait, no, the key is that ∠1 and ∠2 are supplementary? Wait, no, let's see: ∠1 and ∠3 are vertical angles, ∠1 and ∠2 are supplementary (linear pair). But since line x || line y, corresponding angles or consecutive interior? Wait, maybe ∠1 and ∠5 are equal (corresponding), but no, the question is ∠8? Wait, no, the options: 64, 116, 90, 180. Wait, ∠1 and ∠2: linear pair, so ∠1 + ∠2 = 180? No, wait, ∠1 is 64, so if ∠1 and ∠2 are linear pair, ∠2 would be 116, but maybe ∠8? Wait, no, the diagram: line x and y are parallel, transversal. So ∠1 and ∠5: corresponding, so ∠5=64. Then ∠5 and ∠8: vertical angles? No, ∠5 and ∠8: linear pair? Wait, no, maybe ∠1 and ∠4: vertical angles? No, ∠1 and ∠3 are vertical. Wait, maybe the angle in question is ∠8? Wait, no, the options: 64, 116, 90, 180. Wait, ∠1 is 64, so its supplementary angle (linear pair) would be 180 - 64 = 116. So if the angle in question is a supplementary angle to ∠1 (like ∠2 or ∠8 or something), then 116.

Step2: Calculate supplementary angle

Since ∠1 and its supplementary angle (linear pair) sum to 180°, so measure = 180 - 64 = 116 degrees.

Answer:

116 degrees (the option with 116 degrees)