Question

What is 3pi/4 radians converted to degrees? If necessary, round your answer to the nearest degree.

45
135
240
540°

Answer 1

135 degrees

Explanation:

Answer 2

well, we know that 180° = π radians, so what would 3π/4 radians be in degrees then?

`\bf \begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ x&(3\pi )/(4) \end{array}\implies \cfrac{180}{x}=\cfrac{~~\pi ~~}{(3\pi )/(4)}\implies \cfrac{180}{x}=\cfrac{~~(\pi)/(1) ~~}{(3\pi )/(4)} \\\\\\ \cfrac{180}{x}=\cfrac{~~\begin{matrix} \pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }{1}\cdot \cfrac{4}{3~~\begin{matrix} \pi \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~ }\implies \cfrac{180}{x}=\cfrac{4}{3}\implies 540=4x\\\\\\ \cfrac{540}{4}=x\implies 135=x`