Because the three sides of the triangle have equal lengths, we can confirm that the image above represents an equilateral triangle. An equilateral triangle is a triangle whose three sides are the same length and whose three angles are the same measure. We know that the three angles of a triangle must always add to a sum of 180 degrees. With this knowledge, we can create the following equation (let “x” represent the measure of each angle):
x + x + x = 180
Combine like terms:
3x = 180
Divide both sides fo the equation by 3:
x = 60
We have now proven that all three angles of ΔABC have a measure of 60 degrees. Therfore, ∠C must have a measure of 60 degrees.
