Question

The question and answer choices are listed in the picture.

Answer 1

Given:
$L=2 \pi r( \frac{x}{360})$

Solution:
If we want to find the solution for r, we need to move the r to the left side first. So I reverse the side
$2 \pi r( \frac{x}{360})=L$

Move 2π to the right side. Because on the left side 2π acts as numerator, after it's moved to the right side, it becomes denominator.
$2 \pi r( \frac{x}{360})=L$
$r( \frac{x}{360})= \frac{L}{2 \pi }$

Move 360 to the right side. Because on the left side 360 acts as denominator, after it's moved to the right side, it becomes numerator.
$r( \frac{x}{360})= \frac{L}{2 \pi }$
$r(x)= \frac{360L}{2 \pi }$

Move x to the right side. Because on the left side x acts as numerator, after it's moved to the right side, it becomes denominator.
$r(x)= \frac{360L}{2 \pi }$
$r= \frac{360L}{2 \pi x}$

Then simplify the fraction
$r= \frac{360L}{2 \pi x}$
$r= \frac{180L}{ \pi x}$

The answer is second option