A circle measures 360 degrees. If this circle were marked with numbers like a clock, every number would represent 30

Question

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)
• 240 degrees
• 150 degrees
• 120 degrees
• 330 degrees

Answer 1

To determine the degree measure of the angle formed by rotating the angle marker from 11:00 to 4:00, we can start by identifying the degree positions for each of the hour markers.

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

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

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

Next, we find the angle formed by moving from 11:00 to 4:00 in a clockwise direction. Since we are moving from 330 degrees to 120 degrees, we can calculate it as follows:

• Moving clockwise from 330 degrees to 360 degrees completes a full circle: \[ 360 - 330 = 30 \text{ degrees} \]

• We then continue from 0 degrees to 120 degrees: \[ 120 \text{ degrees} \]

Adding these two parts together gives: \[ 30 + 120 = 150 \text{ degrees} \]

Thus, the degree measure of the angle formed moving clockwise from the 11:00 marker to the 4:00 marker is 150 degrees.