Question

How do I convert the angle 3pi/5 radians to degrees?​

Answer 1

since we know there are 180°  in π radians, then, how many in 3π/5?

$\bf \begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\\\ x&\frac{3\pi }{5} \end{array}\implies \cfrac{180}{x}=\cfrac{~~\pi ~~}{\frac{3\pi }{5}}\implies \cfrac{180}{x}=\cfrac{~~\frac{\pi}{1} ~~}{\frac{3\pi }{5}}\implies \cfrac{180}{x}=\cfrac{\pi }{1}\cdot \cfrac{5}{3\pi } \\\\\\ \cfrac{180}{x}=\cfrac{5}{3}\implies 540=5x\implies \cfrac{540}{5}=x\implies 108=x$