The angles of a triangle are in the ratio 3 : 5 : 7. Find each angle in radians and in degrees.

Step 1. The parts. $3 + 5 + 7 = 15$ parts share $\pi$ rad, so one part is $\dfrac{\pi}{15}$ rad, that is $12^\circ$.

Step 2. The angles. $\dfrac{3\pi}{15} = \dfrac{\pi}{5}$, $\dfrac{5\pi}{15} = \dfrac{\pi}{3}$ and $\dfrac{7\pi}{15}$ rad.

Step 3. In degrees. $3 \times 12^\circ = 36^\circ$, $5 \times 12^\circ = 60^\circ$ and $7 \times 12^\circ = 84^\circ$.