Question
What is the degree measure of the angle formed by moving clockwise from 11 o'clock to 4 o'clock on a clock?
Answers
GPT-4o mini
To find the degree measure of the angle formed by moving clockwise from 11 o'clock to 4 o'clock on a clock, we first need to determine the positions of the two times on the clock face.
1. The clock is divided into 12 hours, with a complete circle measuring 360 degrees. Therefore, the angle for each hour is calculated as follows:
\[
\text{Degrees per hour} = \frac{360 \text{ degrees}}{12 \text{ hours}} = 30 \text{ degrees per hour}
\]
2. Next, we find the positions of 11 o'clock and 4 o'clock in terms of their hour marks:
- The position at 11 o'clock corresponds to:
\[
11 \times 30 = 330 \text{ degrees}
\]
- The position at 4 o'clock corresponds to:
\[
4 \times 30 = 120 \text{ degrees}
\]
3. We need to find the angle when moving clockwise from 11 o'clock (330 degrees) to 4 o'clock (120 degrees). Since we are moving clockwise, we can calculate this angle as follows:
- From 11 o'clock (330 degrees) to 4 o'clock (120 degrees), we first move from 330 degrees to 360 degrees (a circular movement), and then from 0 degrees back to 120 degrees.
4. The total clockwise movement is thus:
\[
360 - 330 + 120 = 30 + 120 = 150 \text{ degrees}
\]
Therefore, the angle formed by moving clockwise from 11 o'clock to 4 o'clock is:
\[
\boxed{150} \text{ degrees}
\]
1. The clock is divided into 12 hours, with a complete circle measuring 360 degrees. Therefore, the angle for each hour is calculated as follows:
\[
\text{Degrees per hour} = \frac{360 \text{ degrees}}{12 \text{ hours}} = 30 \text{ degrees per hour}
\]
2. Next, we find the positions of 11 o'clock and 4 o'clock in terms of their hour marks:
- The position at 11 o'clock corresponds to:
\[
11 \times 30 = 330 \text{ degrees}
\]
- The position at 4 o'clock corresponds to:
\[
4 \times 30 = 120 \text{ degrees}
\]
3. We need to find the angle when moving clockwise from 11 o'clock (330 degrees) to 4 o'clock (120 degrees). Since we are moving clockwise, we can calculate this angle as follows:
- From 11 o'clock (330 degrees) to 4 o'clock (120 degrees), we first move from 330 degrees to 360 degrees (a circular movement), and then from 0 degrees back to 120 degrees.
4. The total clockwise movement is thus:
\[
360 - 330 + 120 = 30 + 120 = 150 \text{ degrees}
\]
Therefore, the angle formed by moving clockwise from 11 o'clock to 4 o'clock is:
\[
\boxed{150} \text{ degrees}
\]