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Find the measure of a negative angle coterminal with 180∘180^\circ. \newline____∘^\circ

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Full solution

Q. Find the measure of a negative angle coterminal with 180∘180^\circ. \newline____∘^\circ
  1. Understand coterminal angles: Understand what a coterminal angle is.\newlineCoterminal angles are angles that share the same initial and terminal sides but may have different rotations. They are separated by an integer multiple of 360∘360^\circ (or 2π2\pi radians) for angles measured in degrees (or radians).
  2. Calculate negative coterminal angle: Calculate a negative coterminal angle for 180°180°. To find a negative coterminal angle, we subtract multiples of 360°360° from the given angle until we get a negative result. Since we are starting with 180°180°, we subtract 360°360° once. Calculation: 180°−360°=−180°180° - 360° = -180°
  3. Verify coterminality: Verify that the calculated angle is indeed coterminal with 180°180°. Since we subtracted 360°360°, which is a full rotation, the initial and terminal sides of the angles are the same. Therefore, −180°-180° is coterminal with 180°180°.

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