Show that the angles of an equilateral triangle are 60 degrees each.

To show that the angles of an equilateral triangle are 60 degrees each, we can use the following reasoning:

Definition of an Equilateral Triangle: An equilateral triangle is a triangle in which all three sides are of equal length.

Sum of Interior Angles of a Triangle: The sum of the interior angles of any triangle is always 180 degrees. This is a fundamental property of triangles.

Equal Angles in an Equilateral Triangle: Since all sides of an equilateral triangle are of equal length, all the angles must also be equal. Let's denote each angle of the equilateral triangle as "x".

Setting up the Equation: We know that the sum of the interior angles of a triangle is 180 degrees. In an equilateral triangle, all three angles are equal, so we have the equation:

x + x + x = 180 degrees.

Solving for x: Simplifying the equation:

3x = 180 degrees.

Now, divide both sides of the equation by 3:

x = 180 degrees / 3 = 60 degrees.

Conclusion: Therefore, each angle in an equilateral triangle measures 60 degrees.

This proves that the angles of an equilateral triangle are 60 degrees each.