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? (1 point) Responses 330 degrees 330 degrees 150 degrees 150 degrees 240 degrees 240 degrees 120 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 face, we can follow these steps:

1. Each number on the clock represents a 30-degree increment, since the total circle is 360 degrees divided by 12 hours equals 30 degrees per hour.

2. The position at 11:00 corresponds to:
\[
11 \times 30 = 330 \text{ degrees}
\]

3. The position at 4:00 corresponds to:
\[
4 \times 30 = 120 \text{ degrees}
\]

4. Now, to find the angle moving clockwise from 11:00 to 4:00, we calculate the difference:
\[
\text{Clockwise angle} = \text{Angle at 4:00} - \text{Angle at 11:00}
\]
Since moving clockwise means we wrap around 360 degrees, we have:
\[
\text{Clockwise angle} = 120 \text{ degrees} - 330 \text{ degrees} + 360 \text{ degrees}
\]
\[
= 120 - 330 + 360 = 150 \text{ degrees}
\]

Thus, the degree measure of the angle formed moving clockwise from the position normally marked for 11:00 to the position normally marked for 4:00 is **150 degrees**.