If twice ∠A is subtracted from the supplement of ∠A, then the remaining angle exceeds the complement of ∠A by 4°. Find the size of ∠A.
Let S = 180 – A be the supplement of A, and C = 90 – A be the complement of A. Then:
S – 2A = C + 4
(180 – A) – 2A = (90 – A) + 4
180 – 3A = 94 – A
2A = 86 so A = 43.
Check: If A = 43°, then S = 137° and C = 47°. Does 137 – 2(43) = 47 + 4? Yes.