If the principal angle of (\theta) is (280^\circ), what is the principal angle of (-\theta)?

Correct answer: (80^\circ)

The direct answer is A, \\(80^\circ\\). Coterminal angles differ by a whole turn, \\(360^\circ\\). The given principal angle is \\(280^\circ\\), so the angle represented by \\(-\theta\\) is \\(-280^\circ\\). To express it between \\(0^\circ\\) and \\(360^\circ\\), add one full turn: \\(-280^\circ+360^\circ=80^\circ\\). Option A is correct. Option B, \\(100^\circ\\), would result from using the wrong subtraction, not from negating 280°. Option C, \\(260^\circ\\), is not coterminal with \\(-280^\circ\\), because their difference is not a multiple of 360°. Option D, \\(300^\circ\\), is also unrelated to the required rotation. Geometrically, changing an angle’s sign reflects its terminal arm across the x-axis; the terminal arm at 280° reflects to 80°. Memory cue: for \\(-\theta\\), use \\(360^\circ-\theta\\) when \\(0^\circ<\theta<360^\circ\\).