Question

A circle measures 360 degrees. If this circle were marked with numbers like a clock, every number would represent 30 degrees farther from 0 and closer to 360 degrees. If an angle marker typically found at 11:00 were to rotate to the place normally marked for 4:00, what is the degree measure of the angle formed moving clockwise?

Answer 1

To determine the degree measure of the angle formed when an angle marker at 11:00 moves to the position typically marked for 4:00, we need to calculate the positions of these times in degrees.

First, we find the degree position of 11:00:
- Each hour mark on a clock represents \(30\) degrees since the total degrees in a circle is \(360\), and it is divided into \(12\) hours:
\[
\text{Degrees per hour} = \frac{360}{12} = 30 \text{ degrees}
\]
- Therefore, the position for 11:00 is:
\[
11 \times 30 = 330 \text{ degrees}
\]

Next, we find the degree position for 4:00:
- The position for 4:00 is:
\[
4 \times 30 = 120 \text{ degrees}
\]

Now, to find the angle formed by moving from the 11:00 position (330 degrees) to the 4:00 position (120 degrees) in a clockwise direction, we perform the following calculation:

1. Since moving clockwise means we increase the degree measure, we can compute the angle as follows:

If we consider moving from \(330\) degrees to \(360\) degrees (the end of the circle):
\[
360 - 330 = 30 \text{ degrees}
\]

2. Then, continuing from \(360\) degrees to \(120\) degrees:
\[
120 \text{ degrees}
\]

3. Therefore, the total clockwise movement is:
\[
30 + 120 = 150 \text{ degrees}
\]

Thus, the degree measure of the angle formed moving clockwise from the position typically marked for 11:00 to the position normally marked for 4:00 is:
\[
\boxed{150} \text{ degrees}
\]