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

To find the **reference angle** of \( -260^{\circ} \), follow these steps: ### 1. Understand Reference Angles A *reference angle* is the smallest acute angle (less than \( 90^{\circ} \)) that the terminal side of the given angle makes with the x-axis. Reference angles are always positive, regardless of the original angle's direction (positive or negative). ### 2. Find a Coterminal Angle Between \( 0^{\circ} \) and \( 360^{\circ} \) Since the given angle is negative, it's helpful to find its positive coterminal angle by adding \( 360^{\circ} \): \[ -260^{\circ} + 360^{\circ} = 100^{\circ} \] So, \( 100^{\circ} \) is coterminal with \( -260^{\circ} \) and lies between \( 0^{\circ} \) and \( 360^{\circ} \). ### 3. Determine the Quadrant of the Coterminal Angle \( 100^{\circ} \) lies in the **second quadrant** (between \( 90^{\circ} \) and \( 180^{\circ} \)). ### 4. Calculate the Reference Angle In the second quadrant, the reference angle (\( \theta_{\text{ref}} \)) is calculated as: \[ \theta_{\text{ref}} = 180^{\circ} - \theta \] Where \( \theta \) is the coterminal angle. \[ \theta_{\text{ref}} = 180^{\circ} - 100^{\circ} = 80^{\circ} \] ### **Conclusion** The reference angle of \( -260^{\circ} \) is **\( 80^{\circ} \)**.