Question

a cirlcle 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?
a. 240 degrees
b. 120 degrees
c. 150 degrees
d. 330 degrees

Answer 1

To solve the problem, we first need to determine the positions of the clock numbers in degrees.

1. The position for 11:00 is at \( 11 \times 30 = 330 \) degrees from 0 (12:00 position).
2. The position for 4:00 is at \( 4 \times 30 = 120 \) degrees from 0 (12:00 position).

Now we can find the angle formed by moving clockwise from 330 degrees (11:00) to 120 degrees (4:00):

- Start at 330 degrees and move to 120 degrees in the clockwise direction.

To calculate the clockwise movement:
- Since 330 degrees is greater than 120 degrees, we can find the difference by calculating the clockwise distance as follows:

\[
\text{Clockwise movement} = 360 - 330 + 120 = 30 + 120 = 150 \text{ degrees}
\]

Thus, the angle measured moving clockwise from 11:00 to 4:00 is \( 150 \) degrees.

The correct answer is (c) 150 degrees.