Question

find the reference angle $\theta$. $\theta=-145^{circ}$ $\theta=square^{circ}$ sketch $\theta$ and $\theta$ in standard - position.

Explanation:

Step1: Make the angle positive

Add 360° to - 145° since adding 360° to an angle does not change its terminal - side. $\theta=-145^{\circ}+360^{\circ}=215^{\circ}$.

Step2: Determine the quadrant

The angle 215° lies in the third quadrant (180° < 215° < 270°).

Step3: Calculate the reference angle

For an angle $\theta$ in the third quadrant, the reference angle $\theta'$ is given by $\theta - 180^{\circ}$. So, $\theta'=215^{\circ}-180^{\circ}=35^{\circ}$.

Answer:

35