Question

lines b and c are parallel. what is the measure of ∠2? diagram: transversal a intersects parallel lines b and c. on line b, ∠1 is (7x+1)°, ∠2 is (18x+4)°. on line c, ∠5, ∠6, ∠7, ∠8 are labeled. options: m∠2 = 31°, m∠2 = 50°, m∠2 = 120°, m∠2 = 130°

Explanation:

Step1: Identify supplementary angles

∠1 and ∠2 are supplementary (linear pair), but also, since lines b and c are parallel, ∠1 and ∠6 are equal (corresponding angles), and ∠2 and ∠6 are supplementary? Wait, no, actually ∠1 and ∠2 are adjacent and form a linear pair, so they sum to 180°. Wait, also, ∠1 and ∠5 are equal (corresponding angles), but maybe better: ∠1 and ∠2 are adjacent, so (7x + 1) + (18x + 4) = 180.

Step2: Solve for x

Combine like terms: 7x + 18x + 1 + 4 = 180 → 25x + 5 = 180. Subtract 5: 25x = 175. Divide by 25: x = 7.

Step3: Calculate ∠2

Substitute x = 7 into ∠2's expression: 18x + 4 = 187 + 4 = 126 + 4 = 130? Wait, no, wait: Wait, ∠1 is (7x +1), ∠2 is (18x +4). Wait, but if lines b and c are parallel, then ∠1 and ∠5 are equal, and ∠5 and ∠6 are supplementary? Wait, maybe I made a mistake. Wait, actually, ∠1 and ∠2 are adjacent angles on a straight line, so they must be supplementary. So (7x +1) + (18x +4) = 180. So 25x +5 = 180 → 25x=175 → x=7. Then ∠2 is 187 +4 = 130? Wait, but let's check: 7x +1 = 7*7 +1=50. 50 +130=180, which works. So ∠2 is 130 degrees.

Answer:

m∠2 = 130°