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Solve for x in the triangle with angles 3x, 2x - 20, and 60 degrees.

Mathematics

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Answer

28∘\text{28}^\circ

Step-by-step solution

5 steps
  1. The sum of the interior angles in a triangle is 180∘180^\circ.

    We are given the three angles of the triangle as 3x3x, 2x−20∘2x - 20^\circ, and 60∘60^\circ.

  2. Set up the equation for the sum of the angles.

    3x+(2x−20∘)+60∘=180∘3x + (2x - 20^\circ) + 60^\circ = 180^\circ
  3. Combine like terms.

    5x+40∘=180∘5x + 40^\circ = 180^\circ
  4. Isolate the term with xx.

    Subtract 40∘40^\circ from both sides of the equation.

    5x=180∘−40∘5x = 180^\circ - 40^\circ 5x=140∘5x = 140^\circ
  5. Solve for xx.

    Divide both sides by 5.

    x=140∘5x = \frac{140^\circ}{5} x=28∘x = 28^\circ

    The value of xx is 28∘\boxed{\text{28}^\circ}.

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