Final answer:
The hour hand of a clock moves through 120 degrees when it goes from 10 to 2 o'clock, calculated by multiplying the number of hours (4) by the degrees per hour (30), which gives us 4 hours x 30 degrees/hour.
Step-by-step explanation:
The question pertains to the concept of angles and their measurement in the context of clock arithmetic. Specifically, we are asked to determine the angle through which the hour hand of a clock moves when it goes from 10 to 2 o'clock. We know that a full rotation of a clock's hour hand is 360 degrees, which corresponds to 12 hours. To find the degree measurement of an hour, we simply divide 360 degrees by 12, yielding 30 degrees per hour.
Since the hour hand moves from 10 to 2, it covers 4 hours which is calculated as follows:
• From 10 to 11 = 1 hour
• From 11 to 12 = 1 hour
• From 12 to 1 = 1 hour
• From 1 to 2 = 1 hour
This amounts to a total of 4 hours. To find the number of degrees the hour hand has moved, we multiply the number of hours (4) by the degrees per hour (30 degrees).
4 hours × 30 degrees/hour = 120 degrees
Therefore, when the hour hand moves from 10 to 2 o'clock, it travels through an angle of 120 degrees. The correct answer is option (a).