Question

The measure of angle A is 140°. What is the measure of this angle in radians?

A. Pi/14
B. 7/pi
C. 14pi radians
D. 7pi/9

Answer 1

well, we know that 180° is π radians, so how many radians in 140°?

`\begin{array}{ccll} degrees&radians\\ \cline{1-2} 180&\pi \\ 140&x \end{array}\implies \cfrac{180}{140}~~ = ~~\cfrac{\pi }{x} \\\\\\ \cfrac{9}{7}~~ = ~~\cfrac{\pi }{x}\implies 9x=7\pi \implies x=\cfrac{7\pi }{9}`