Find the Reference Angle 105 degrees

Problem

105^∘

Solution

1. Identify the quadrant in which the given angle θ=105^∘ lies. Since 90^∘<105^∘<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 to calculate the result.

4. Subtract the values: 180^∘−105^∘=75^∘

Final Answer

θ^′=75^∘

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