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?

(1 point)
Responses

-240 degrees
-240 degrees

240 degrees
240 degrees

-150 degrees
-150 degrees

150 degrees

1 answer

To determine the degree measure of the angle formed when the angle marker at 11:00 rotates to the position normally marked for 4:00, we first need to find the degree representations for both of these positions.

Each hour on a clock represents 30 degrees since \(360 \text{ degrees} / 12 \text{ hours} = 30 \text{ degrees per hour}\).

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

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

Now, we find the angle formed when moving from the 11:00 position (330 degrees) to the 4:00 position (120 degrees).

  1. To determine the angle in the standard positive direction (counterclockwise), we subtract: \[ 120 - 330 = -210 \text{ degrees} \] Since angles are often represented in positive values, we can convert this negative angle into a positive one by adding 360 degrees: \[ -210 + 360 = 150 \text{ degrees} \]

Thus, the measure of the angle formed when the angle marker at 11:00 rotates to the position for 4:00 is 150 degrees.

The correct answer is:

  • 150 degrees