The supplement of <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mn>105</mn><mo>)</mo></mrow></mstyle></math> is the angle that when added to <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mn>105</mn><mo>)</mo></mrow></mstyle></math> forms a straight angle (<math><mstyle displaystyle="true"><mn>180</mn><mi>°</mi></mstyle></math> ).

Apply the reference angle by finding the angle with equivalent trig values in the first quadrant. Make the expression negative because tangent is negative in the second quadrant.

Evaluate <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mn>75</mn><mo>)</mo></mrow></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mn>3.7320508</mn></mstyle></math> .

Multiply <math><mstyle displaystyle="true"><mo>-</mo><mn>1</mn></mstyle></math> by <math><mstyle displaystyle="true"><mo>-</mo><mn>3.7320508</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>3.7320508</mn></mstyle></math> .

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