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 4:00, what is the degree measure of the angle formed moving clockwise? (1 point) Responses 150 degrees 150 degrees 120 degrees 120 degrees 330 degrees 330 degrees 240 degrees

Answer 1

To find the degree measure of the angle formed when moving clockwise from 11:00 to 4:00 on a circle marked like a clock, we can follow these steps:

1. Determine the degree position of 11:00 and 4:00:

   • Each hour on a clock represents 30 degrees (since \(360\) degrees / \(12\) hours = \(30\) degrees/hour).
   • 11:00 corresponds to \(11 \times 30 = 330\) degrees.
   • 4:00 corresponds to \(4 \times 30 = 120\) degrees.

2. Calculate the angle moving clockwise from 11:00 (330 degrees) to 4:00 (120 degrees):

   • Since we are moving clockwise from 330 degrees back around to 120 degrees, we can calculate it as follows:
   • The angle from \(330\) degrees to \(360\) degrees is \(360 - 330 = 30\) degrees.
   • Then, from \(0\) degrees to \(120\) degrees is \(120 - 0 = 120\) degrees.
   • Therefore, the total angle moving clockwise is \(30 + 120 = 150\) degrees.

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