If in radians the complement of an angle is \(\frac{1}{3}\) of its supplement then what is the angle?

Correct answer: \(\frac{\pi}{4}\)

Let the angle be \(x\) radians. Its complement is \(\frac{\pi}{2}-x\), and its supplement is \(\pi-x\). From the condition, \(\frac{\pi}{2}-x=\frac{1}{3}(\pi-x)\). Multiplying by 3 gives \(\frac{3\pi}{2}-3x=\pi-x\). Hence \(\frac{\pi}{2}=2x\), so \(x=\frac{\pi}{4}\). Thus, option B is correct. For the close distractor \(\frac{\pi}{3}\), the complement is \(\frac{\pi}{6}\) and the supplement is \(\frac{2\pi}{3}\); the complement is \(\frac{1}{4}\), not \(\frac{1}{3}\), of the supplement. Exam tip: use \(\frac{\pi}{2}\) for complement and \(\pi\) for supplement when working in radians.