Line and segment relationship in the circle if the larger gear has 30 teeth and the smaller gear has 18, then the gear ratio(larger to smaller) is 5:3. when the larger gear rotates through and of 60°, through what angel measure does the smaller gear rotate? 

The angle between two teeth in the lager gear is $\frac {360°}{30}=12°$ and for smaller gear is $\frac {360°}{18}=20°$. When the larger gear rotates for $60°$ it means $5$ teeth has moved $(\frac {60°}{12°}=5)$. Because these gears are connected then the smaller gear must move for $5$ teeth too, and $5$ teeth in smaller gear means $5\times 20°=100°$, so the smaller gear will rotate for $100$ degrees.
