What value between 0 and 360 degrees expresses the same angle as 960 degrees?
The correct answer and explanation is:
To find an angle between 0 and 360 degrees that is equivalent to 960 degrees, you need to reduce the angle within one full rotation of a circle. A full circle has 360 degrees, so to get an equivalent angle, you will subtract multiples of 360 from 960 until the angle falls within the 0 to 360-degree range.
First, divide 960 by 360 to determine how many full rotations fit into 960 degrees: 960÷360=2.6667960 \div 360 = 2.6667
This means that 960 degrees is a bit more than two full rotations. To find the equivalent angle, subtract the product of 360 and the integer part of the quotient (2 full rotations) from 960: 960−(360×2)=960−720=240960 – (360 \times 2) = 960 – 720 = 240
So, 960 degrees is equivalent to 240 degrees in the 0 to 360-degree range.
In general, when you are asked to find an equivalent angle within one full rotation of a circle, you use the following formula: Equivalent angle=Original anglemod 360\text{Equivalent angle} = \text{Original angle} \mod 360
For 960 degrees, the calculation would be: 960mod 360=240960 \mod 360 = 240
This shows that 960 degrees and 240 degrees represent the same direction or angle in a circle, both ending at the same point. The remainder of the division is the answer, and 240 degrees is the final equivalent angle.