The difference between two angles is 15^\circ and the sum of the angles in radian is \frac{5\pi}{12}. The bigger angle is k times the smaller angle. What is k equal to?

Explanation

Let the angles be A and B. 15^\circ in radians is \frac{\pi}{12}. We have A - B = \frac{\pi}{12} and A + B = \frac{5\pi}{12}. Adding them gives 2A = \frac{6\pi}{12} = \frac{\pi}{2}, so A = \frac{\pi}{4} = 45^\circ. Subtracting them gives 2B = \frac{4\pi}{12} = \frac{\pi}{3}, so B = \frac{\pi}{6} = 30^\circ. The ratio k = \frac{A}{B} = \frac{45}{30} = \frac{3}{2}.

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