Find an angle in each quadrant with a common reference angle with 307°, from 0°≤θ<360°

Sure, let's find the angles in each quadrant that have the same reference angle as 307°.

First, we need to find the reference angle for 307°. The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. For an angle in the fourth quadrant like 307°, the reference angle can be found by subtracting the angle from 360°.

360° - 307° = 53°

So, the reference angle is 53°.

Now, we need to find an angle in each quadrant that has this same reference angle.

1. In the first quadrant, the angle is simply the reference angle itself, so it's 53°.

2. In the second quadrant, the angle can be found by subtracting the reference angle from 180°. 180° - 53° = 127°

3. In the third quadrant, the angle can be found by adding the reference angle to 180°. 180° + 53° = 233°

4. In the fourth quadrant, the angle is the original angle we were given, 307°.

So, the angles in each quadrant that have the same reference angle as 307° are 53°, 127°, 233°, and 307°.