Find the Reference Angle 165

Problem

165^∘

Solution

1. Identify the quadrant in which the given angle θ=165^∘ lies. Since 90^∘<165^∘<180^∘ the angle is in Quadrant II.

2. Apply the formula for the reference angle θ^′ in Quadrant II, which is θ^′=180^∘−θ

3. Substitute the value of the angle into the formula: θ^′=180^∘−165^∘

4. Subtract the values to find the reference angle.

Final Answer

θ^′=15^∘

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