Question

Convert the following into degree measure: 7pi/12

Answer 1

Since we know that there are 180° in π radians, then, how many degrees are there in 7π/12 radians?

$\bf \begin{array}{ccll} de grees&radians\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 180&\pi \\\\ d&\frac{7\pi }{12} \end{array}\implies \cfrac{180}{d}=\cfrac{\quad \pi \quad }{\frac{7\pi }{12}}\implies \cfrac{180}{d}=\cfrac{\quad \frac{\pi}{1} \quad }{\frac{7\pi }{12}} \\\\\\ \cfrac{180}{d}=\cfrac{\underline{\pi} }{1}\cdot \cfrac{12}{7\underline{\pi} }\implies \cfrac{180}{d}=\cfrac{12}{7}\implies \cfrac{180\cdot 7}{12}=d\implies 105=d$