Find the Reference Angle -135 degrees

Problem

−135

Solution

1. Find the coterminal angle between 0 and 360 by adding 360 to the given negative angle.

−135+360=225

2. Identify the quadrant where the terminal side of the angle lies. Since 180<225<270 the angle is in Quadrant III.

225∈Quadrant III

3. Apply the reference angle formula for Quadrant III, which is θ′=θ−180

θ′=225−180

4. Calculate the result to find the positive acute angle formed with the x-axis.

θ′=45

Final Answer

θ′=45

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