If (72^\circ) is converted into radians and written as (\frac{k\pi}{5}), what is (k)?

Correct answer: (2)

The direct answer is option B: k = 2. To convert degrees to radians, multiply by \(\frac{\pi}{180^\circ}\). Thus, \(72^\circ\times\frac{\pi}{180^\circ}=\frac{72\pi}{180}=\frac{2\pi}{5}\), after dividing numerator and denominator by 36. Comparing this result with the required form \(\frac{k\pi}{5}\), the numerator shows that k = 2. Option A, 1, is wrong because \(\frac{\pi}{5}\) equals 36°, not 72°. Option B, 2, is correct because \(\frac{2\pi}{5}\) equals 72°. Option C, 3, would give \(\frac{3\pi}{5}=108^\circ\), which is too large. Option D, 4, would give \(\frac{4\pi}{5}=144^\circ\), also too large. Always simplify the fraction after converting; the coefficient of π is the required k. A useful memory pair is 180° = π radians, so degrees-to-radians uses π/180.