Question

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 6:00, what is the degree measure of the angle formed moving CLOCKWISE? (1 point) Responses 210 degrees 210 degrees 150 degrees 150 degrees 120 degrees 120 degrees 330 degrees

Answer 1

To find the degree measure of the angle formed by moving the angle marker from 11:00 to 6:00 clockwise, we first determine the degree position of the two times on a clock.

• The position of 11:00 corresponds to:
  \(11 \times 30 = 330\) degrees (since each hour represents 30 degrees).

• The position of 6:00 corresponds to:
  \(6 \times 30 = 180\) degrees.

Now, to find the angle formed by moving clockwise from 11:00 to 6:00, we can calculate it as follows:

1. Start at 330 degrees.
2. Move clockwise to 180 degrees.

Since 330 degrees is greater than 180 degrees, we compute the clockwise angle by subtracting the smaller angle (6:00 position) from the larger angle (11:00 position):

\[ \text{Clockwise angle} = 360 - 330 + 180 = 210 \text{ degrees}. \]

Thus, the degree measure of the angle formed moving clockwise from 11:00 to 6:00 is:

210 degrees.