Question

find the reference angle of the angle. - 175° the reference angle for - 175° is (square^{circ}).

Explanation:

Step1: Make the angle positive

Add $360^{\circ}$ to the negative angle. Since $- 175^{\circ}+360^{\circ}=185^{\circ}$, the equivalent positive - angle is $185^{\circ}$.

Step2: Determine the quadrant

The angle $185^{\circ}$ lies in the third - quadrant ($180^{\circ}<185^{\circ}<270^{\circ}$).

Step3: Calculate the reference angle

For an angle $\theta$ in the third - quadrant, the reference angle $\theta_{r}=\theta - 180^{\circ}$. So, for $\theta = 185^{\circ}$, $\theta_{r}=185^{\circ}-180^{\circ}=5^{\circ}$.

Answer:

$5$