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

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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 **$$ 80^{\circ} $$**.
The reference angle of $$ -260^{\circ} $$ is $$ 80^{\circ} $$.

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

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