Find an angle in each quadrant with a common reference angle with 118°, from 0°≤θ<360°

Sure, let's find the angles in each quadrant that have the same reference angle as 118°.

1. 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 in the standard position, its reference angle is the smallest angle it makes with the x-axis.

   For 118°, the reference angle is 180° - 118° = 62°.

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

   • For Quadrant I, the angle is simply the reference angle itself, which is 62°.

   • For Quadrant II, the angle is 180° - reference angle = 180° - 62° = 118°.

   • For Quadrant III, the angle is 180° + reference angle = 180° + 62° = 242°.

   • For Quadrant IV, the angle is 360° - reference angle = 360° - 62° = 298°.

So, the angles in each quadrant that have the same reference angle as 118° are 62°, 118°, 242°, and 298°.