Find an angle in each quadrant with a common reference angle with 337°, from 0°≤θ<360°

Sure, let's find the angles.

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 337°, the reference angle is found by subtracting from 360° because it's in the fourth quadrant. So, 360° - 337° = 23°.

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 same as the reference angle, so it's 23°.

2. In the second quadrant, we subtract the reference angle from 180°. So, 180° - 23° = 157°.

3. In the third quadrant, we add the reference angle to 180°. So, 180° + 23° = 203°.

4. In the fourth quadrant, we subtract the reference angle from 360°. So, 360° - 23° = 337°.

So, the angles in each quadrant with the same reference angle as 337° are 23°, 157°, 203°, and 337°.