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∠1 and ∠2 are a linear pair. m∠1=x-33, and m∠2=x+71. Find the measure of each angle.

Linear pair are two angles that are adjacent (share a leg) and supplementary (add up to 180°).

We have m∠1 = x - 33 and m∠2 = x + 71. Make and solve the equation:

(x - 33) + (x + 71) = 180

(x + x) + (-33 + 71) = 180

2x + 38 = 180 subtract 38 from both sides

2x = 142 divide both sides by 2

x = 71

m∠1 = x - 33 → m∠1 = 71 - 33 = 38

m∠2 = x + 71 → m∠2 = 71 + 71 = 142

Answer: m∠1 = 38° and m∠2 = 142°