Find an angle in each quadrant with a common reference angle with 255°, from 0°≤θ<360°

Sure, let's find the angles in each quadrant that have the same reference angle as 255°.

First, we need to find the reference angle. The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. For an angle of 255°, the reference angle is 255° - 180° = 75°.

Now, let's find an angle in each quadrant that has this same reference angle.

1. Quadrant I: In the first quadrant, the angle with the same reference angle is simply the reference angle itself, 75°.

2. Quadrant II: In the second quadrant, the angle with the same reference angle is 180° - 75° = 105°.

3. Quadrant III: In the third quadrant, the angle with the same reference angle is 180° + 75° = 255°. This is the original angle we were given.

4. Quadrant IV: In the fourth quadrant, the angle with the same reference angle is 360° - 75° = 285°.

So, the angles in each quadrant that have the same reference angle as 255° are 75°, 105°, 255°, and 285°.