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Given the image with a triangle, find the value of x.

Mathematics

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Answer

x=60∘x = 60^\circ

Step-by-step solution

3 steps

  1. Identify the properties of the triangle.

    The image shows a triangle where all three interior angles are marked with the same symbol (an arc with a single line). This notation indicates that all three angles are equal. Therefore, the triangle is an equilateral triangle.

  2. Apply the angle sum property of a triangle.

    The sum of the interior angles in any triangle is 180∘180^\circ. Since all three angles are equal to xx, we can set up the equation:

    x+x+x=180∘x + x + x = 180^\circ

  3. Solve for xx.

    Combine the terms on the left side of the equation:

    3x=180∘3x = 180^\circ

    Divide both sides by 3 to find the value of xx:

    x=180∘3x = \frac{180^\circ}{3} x=60∘x = 60^\circ

    The value of xx is 60∘60^\circ.

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