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

Answer 1

To determine the degree measure of the angle formed when moving clockwise from the 11:00 position to the 4:00 position on a clock, we first need to calculate the degree positions of both times.

Each hour mark on a clock represents \(30\) degrees (because \(360\) degrees / \(12\) hours = \(30\) degrees/hour).

- The position for 11:00 is:
\[
11 \times 30 = 330 \text{ degrees}
\]

- The position for 4:00 is:
\[
4 \times 30 = 120 \text{ degrees}
\]

Now, we need to find the clockwise angle from 11:00 (330 degrees) to 4:00 (120 degrees).

To do this, we can calculate the angle moved clockwise as follows:
1. Start at \(330\) degrees (11:00) and move directly to \(120\) degrees (4:00).
2. Since \(120\) degrees is less than \(330\) degrees, we need to complete a full rotation back to \(120\) degrees.

Now, calculate the clockwise angle:
\[
\text{Angle} = 360 - 330 + 120 = 30 + 120 = 150 \text{ degrees}
\]

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