You can start by converting from degrees to radians and using the relation
[tex]L=r\theta=\dfrac12d\theta[/tex]
Or just set up the proportion equation,
[tex]\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}[/tex]
