explain how you can use the triangle sum theorem to find the measures of the angles of an equilateral triangle

Question

explain how you can use the triangle sum theorem to find the measures of the angles of an equilateral triangle

Answer 1

The triangle sum theorem says that the sum of all three angle measures of any triangle is 180º. In other words, in triangle ABC, m<A + m<B + m<C = 180º.

 

In an equilateral triangle, all angles have the same measure. Call that angle measure x. Using the triangle sum theorem, we know that:

 

x + x + x = 180º

 

Solve for x to find the measures of the angles of the equilateral triangle:

 

3x = 180º

x = 60º

 

This is why all equilateral triangles have angles measuring 60º.