To determine the measure of the arc between the numbers 7 and 4 on a clock face, follow these steps:
1. Understand the Clock Face:
- A clock face is a circle divided into 12 equal segments, each representing an hour.
2. Degrees per Hour:
- Each hour represents [tex]\(\frac{360^\circ}{12} = 30^\circ\)[/tex].
3. Determine the Hour Positions:
- Identified hours on the clock face are 7 and 4.
4. Calculate the Difference in Hours:
- Calculate the absolute difference: [tex]\(|7 - 4| = 3\)[/tex].
5. Find the Smaller Angle:
- The maximum hour difference is 12/2 = 6. Since 3 is less than 6, we use the hour difference directly.
6. Arc Measure:
- Multiply the hour difference by the degrees per hour: [tex]\(3 \times 30^\circ = 90^\circ\)[/tex].
So, the measure of the arc represented by the numbers 7 and 4 on a clock face is [tex]\(\boxed{90^\circ}\)[/tex].
