The angle created by two hands of a clock when the clock shows 5.20 P.M. is :

In a clock, 

In one revolution the minute hand covers 60°

$$\Rightarrow$$ 60 minutes = 360°

$$\Rightarrow$$ 1 minute = 6°.

$$\Rightarrow$$ for every minute the minute hand covers 6°.

Similarly In one revolution the hour hand covers 12 hours.

$$\Rightarrow$$ 12 hours = 360°

$$\Rightarrow$$ 1 hour = 30°.

$$\Rightarrow$$ for every hour, the hour hand covers 30°.

So at 5.20 P.M. the hour hand must have covered 5 * 30° = 150° + 20*1/2 = 160

and minute hand must have covered 20 * 6° = 120°.

So the angle created by two hands of the clock when the time is 5.20 P.M. = 160 - 120 = 40°.