Use the image to answer the question.
A circle is divided into 12 equal segments by 12 lines emanating from the center. With the exception of 120 degrees and 330 degrees, all of the segments are labeled in 30-degree increments. At 120 degrees and 330 degrees, the segments are labeled as time on a clock.
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?
To find the degree measure of the angle formed moving clockwise from 11:00 to 4:00, we need to calculate the difference between these two points on the circle.
From 11:00 to 12:00, there is a 30-degree increment. From 12:00 to 4:00, there are 4 increments of 30 degrees each, totaling 120 degrees.
So, the angle formed moving clockwise from 11:00 to 4:00 is 30 degrees + 120 degrees = 150 degrees.
To find the degree measure of the angle formed by moving the angle marker from 11:00 to 4:00, we need to calculate the difference between these two positions.
From the image, we can see that the angle marker at 11:00 is labeled as 330 degrees on the circle. The angle marker at 4:00 is not labeled directly, but we know it is on the segment between the 4:00 and the 5:00 positions.
Since each segment is labeled in 30-degree increments, the segment between 4:00 and 5:00 represents 30 degrees. Therefore, the angle marker at 4:00 is at 360 degrees - 30 degrees = 330 degrees.
Now, we can calculate the difference between 330 degrees (11:00) and 330 degrees (4:00):
330 degrees (11:00) - 330 degrees (4:00) = 0 degrees.
Therefore, the degree measure of the angle formed by moving the angle marker from 11:00 to 4:00, clockwise, is 0 degrees.
To find the degree measure of the angle formed when the angle marker typically found at 11:00 rotates to the place normally marked for 4:00, we need to determine the clockwise distance between these two positions on the circle.
First, let's identify the degree measure for each position. From the information given, we know that the segments are labeled in 30-degree increments. The segment at 11:00 is labeled as 330 degrees, while the segment at 4:00 is labeled as 120 degrees.
To find the clockwise distance between these two positions, we subtract the degree measures:
120 degrees - 330 degrees = -210 degrees
However, we need to consider that angles can be measured either clockwise or counterclockwise. In this case, we are interested in the clockwise direction. Since a full circle measures 360 degrees, we can add 360 degrees to ensure a positive clockwise measure:
-210 degrees + 360 degrees = 150 degrees
Therefore, the degree measure of the angle formed when the angle marker rotates from 11:00 to 4:00 clockwise is 150 degrees.