Add <math><mstyle displaystyle="true"><mn>360</mn><mi>°</mi></mstyle></math> to <math><mstyle displaystyle="true"><mo>-</mo><mn>580</mn><mi>°</mi></mstyle></math> .

The resulting angle of <math><mstyle displaystyle="true"><mo>-</mo><mn>220</mn><mi>°</mi></mstyle></math> is coterminal with <math><mstyle displaystyle="true"><mo>-</mo><mn>580</mn><mi>°</mi></mstyle></math> but isn't positive. Repeat the step.

Add <math><mstyle displaystyle="true"><mn>360</mn><mi>°</mi></mstyle></math> to <math><mstyle displaystyle="true"><mo>-</mo><mn>220</mn><mi>°</mi></mstyle></math> .

The resulting angle of <math><mstyle displaystyle="true"><mn>140</mn><mi>°</mi></mstyle></math> is positive and coterminal with <math><mstyle displaystyle="true"><mo>-</mo><mn>580</mn><mi>°</mi></mstyle></math> .

Since the angle <math><mstyle displaystyle="true"><mn>140</mn><mi>°</mi></mstyle></math> is in the second quadrant, subtract <math><mstyle displaystyle="true"><mn>140</mn><mi>°</mi></mstyle></math> from <math><mstyle displaystyle="true"><mn>180</mn><mi>°</mi></mstyle></math> .

Subtract <math><mstyle displaystyle="true"><mn>140</mn></mstyle></math> from <math><mstyle displaystyle="true"><mn>180</mn></mstyle></math> .

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