Question

26.) $\theta=-135^{circ}\to$ reference angle: ____________

Explanation:

Step1: Make the angle positive

Since the given angle $\theta=- 135^{\circ}$, we add $360^{\circ}$ to it. $\theta=-135^{\circ}+360^{\circ}=225^{\circ}$.

Step2: Determine the quadrant

The angle $225^{\circ}$ lies in the third - quadrant ($180^{\circ}<225^{\circ}<270^{\circ}$).

Step3: Calculate the reference angle

For an angle $\theta$ in the third - quadrant, the reference angle $\theta_{r}=\theta - 180^{\circ}$. So, $\theta_{r}=225^{\circ}-180^{\circ}=45^{\circ}$.

Answer:

$45^{\circ}$