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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