Find an angle in each quadrant with a common reference angle with 144°, from 0°≤θ<360°

Sure, let's find the angles in each quadrant that have the same reference angle as 144°.

Step 1: Find the reference angle The reference angle is the acute angle that the terminal side of the given angle makes with the x-axis. For an angle in the second quadrant like 144°, the reference angle (r) can be found using the formula r = 180° - θ. So, r = 180° - 144° = 36°.

Step 2: Find the angle in each quadrant Now, we'll find an angle in each quadrant that has the same reference angle (36°).

• Quadrant I: The angle is the same as the reference angle, so it's 36°.
• Quadrant II: The angle is 180° - reference angle = 180° - 36° = 144°.
• Quadrant III: The angle is 180° + reference angle = 180° + 36° = 216°.
• Quadrant IV: The angle is 360° - reference angle = 360° - 36° = 324°.

So, the angles in each quadrant that have the same reference angle as 144° are 36°, 144°, 216°, and 324°.