Type your answer What is the reference angle of the angle \( -260^{\circ} \) ? W out

To find the reference angle of an angle, we follow these steps: 1. **Convert the negative angle to a positive angle**: Since angles are typically measured in a positive direction, we can add \(360^{\circ}\) to the negative angle until we get a positive angle. \[ -260^{\circ} + 360^{\circ} = 100^{\circ} \] 2. **Determine the reference angle**: The reference angle is the acute angle formed by the terminal side of the given angle and the x-axis. For angles in the second quadrant (which \(100^{\circ}\) is), the reference angle \(r\) can be found using the formula: \[ r = 180^{\circ} - \theta \] where \(\theta\) is the positive angle. \[ r = 180^{\circ} - 100^{\circ} = 80^{\circ} \] Thus, the reference angle of \( -260^{\circ} \) is \( 80^{\circ} \).