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Mathematics

An angle is 80° less than three times its supplement. The angle is

  1. 75°
  2. 85°
  3. 105°
  4. 115°

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Answer

Let the supplement be s.

The angle is (3s - 80°)

Since they are supplementary:

(3s - 80°) + s = 180°

⇒ 4s - 80° = 180°

⇒ 4s = 180° + 80°

⇒ 4s = 260°

⇒ s = 260∘4\dfrac{260^\circ}{4}

⇒ s = 65°

The angle = 180° - 65° = 115°

Hence, option 4 is the correct option.

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