In which quadrant does the angle 795 degrees lie?
We begin by recalling that the 𝑥𝑦-coordinate plane is split into four quarters called quadrants as shown. They are labeled in a counterclockwise direction from the positive 𝑥-axis. And angles in standard position are measured in the same way. There are 360 degrees in a full turn. So we can label 90, 180, 270, and 360 degrees on our diagram.
In this question, our angle is greater than 360, so we’ll need to go around more than once. Two complete turns is equal to 720 degrees. So we can add 450, 540, 630, and 720 degrees to our diagram. Moving another quarter turn would take us to 810 degrees. And 795 degrees is less than this. This means that the terminal line of our angle will lie in the first quadrant. And we can therefore conclude that the angle 795 degrees lies in the first quadrant.