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?

A. 150 degrees
B. 240 degrees
C. 120 degrees
D. 330 degrees

Answer 1

To solve the problem, we first need to determine the degree measures for both the 11:00 position and the 4:00 position on the clock.

1. The positions on a clock represent the following degree measures:
- Each hour marks 30 degrees because \( \frac{360 \text{ degrees}}{12 \text{ hours}} = 30 \text{ degrees/hour} \).

2. The 11:00 position:
- To find the degree measure for 11:00:
\[
11 \times 30 = 330 \text{ degrees}
\]

3. The 4:00 position:
- To find the degree measure for 4:00:
\[
4 \times 30 = 120 \text{ degrees}
\]

4. Next, we calculate the clockwise angle formed when moving from the 11:00 position (330 degrees) to the 4:00 position (120 degrees).
- Since we are moving clockwise, we can simply subtract the two angle measures:
\[
120 \text{ degrees} - 330 \text{ degrees} = -210 \text{ degrees}
\]
- Since this is a negative angle (indicating a clockwise rotation), we can find the equivalent positive angle by adding 360 degrees:
\[
-210 + 360 = 150 \text{ degrees}
\]

Thus, the degree measure of the angle formed moving clockwise from the 11:00 position to the 4:00 position is:

\[
\boxed{150} \text{ degrees}
\]