Answer:
At 5:10 PM, the minute hand is at the 2-minute mark, and the hour hand is between the 5 and 6 marks, closer to the 5.
The minute hand is at the 2-minute mark, which is 1/30th of the way around the clock face. So, the minute hand has traveled 1/30th of a full circle, which is 360°, or 12°.
The hour hand is between the 5 and 6 marks, closer to the 5. It has passed the 5 and is 1/6th of the way to the 6. Since the clock face is divided into 12 hours, 1/6th of the way from 5 to 6 is 5 + 1/6 = 5.166... hours.
Each hour mark represents 30 degrees, so the hour hand has traveled 5.166... × 30 = 155 degrees from the 12 o'clock position.
The smaller angle between the hands is the angle between the hour hand and the minute hand that is less than 180 degrees. We can find this angle by subtracting the smaller angle between the hands from 360 degrees.
To find the smaller angle between the hands, we can subtract the angle traveled by the hour hand from the angle traveled by the minute hand:
12° - 155° = -143°
The negative sign indicates that the angle is measured clockwise from the 12 o'clock position. To find the positive angle between the hands, we add 360 degrees:
360° - 143° = 217°
Therefore, the degree measure of the smaller angle between the hour and minute hands of the clock at 5:10 PM is approximately 217 degrees. Since this value is not one of the answer choices, we can round it to the nearest choice, which is F. 110°