The angle between the hour hand and the minute hand of a clock can be calculated by determining the difference between their positions. In this case, the minute hand is at 2 and the hour hand is between 3 and 4. To calculate the exact angle, we need to determine the fraction of the hour that has passed.

Since 10 minutes have passed since 3 o`clock, it means that 1/6th of an hour has passed (10 minutes divided by 60 minutes in an hour). This means that the hour hand is 1/6th of the way between 3 and 4.

To calculate the angle, we can determine the total angle between 3 and 4 (which is 30 degrees since each hour is divided into 12 equal parts, resulting in 360 degrees for the entire clock). We then multiply this total angle by the fraction of the hour that has passed (1/6).

Using this calculation, we find that the angle between the hour hand and the minute hand at 10 minutes past 3 is 30 degrees multiplied by 1/6, which equals 5 degrees.

Therefore, option 2 (35 degrees) is the correct answer.