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?

Question

(1 point)
Responses

-240 degrees
-240 degrees

240 degrees
240 degrees

-150 degrees
-150 degrees

150 degrees
150 degrees

Answer 1

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

1. Position of 11:00:

   • Each hour on a clock represents 30 degrees (360 degrees / 12 hours).
   • Therefore, 11:00 is at \(11 \times 30 = 330\) degrees.

2. Position of 4:00:

   • Similarly, 4:00 is at \(4 \times 30 = 120\) degrees.

Now, we can find the angle formed by the rotation from 11:00 to 4:00:

• The difference in degrees when rotating from 330 degrees to 120 degrees can be calculated: \[ 120 - 330 = -210 \text{ degrees} \]

The angle measured in the clockwise direction needs to be added to complete the circle, hence: \[ 360 - 210 = 150 \text{ degrees} \]

Thus, the angle formed is 150 degrees.

So, the correct response is: 150 degrees