In a clock having a circular scale of twelve hours, when time changes from 7:45 A.M. to 7:47 A.M., by how many degrees the angle formed by the hour hand and minute hand changes?

Angle covered by the hour hand in 12 hours = 360°

In 1 hour = $$\frac{360}{12} = 30^{\circ}$$

and in 1 minute = $$\frac{30}{60} = \frac{1}{2}^{\circ}$$

Similarly, angle covered by minute hand in 1 hour = 360°

In 1 minute = $$\frac{360}{60} = 6^{\circ}$$

=> Every minute, the angle between the two hands changes by = $$6 - \frac{1}{2} = \frac{11}{2}^{\circ}$$

$$\therefore$$ From 7:45 A.M. to 7:47 A.M.,i.e. in 2 minutes the angle between the two hands will change by

= $$2 \times \frac{11}{2} = 11^{\circ}$$