Question

The 190° arc measures 25 mm. What is the diameter of the entire circle?

Answer 1

You can start by converting from degrees to radians and using the relation

$L=r\theta=\dfrac12d\theta$

Or just set up the proportion equation,

$\dfrac{\text{arc length}}{\text{circumference}}=\dfrac{25\text{ mm}}{180^\circ d}=\dfrac{190^\circ}{360^\circ}=\dfrac{\text{angle subtended by arc}}{\text{one revolution}}\implies d=\dfrac5{19}$