Determine whether this statement is true or false: the angles of the equilateral triangle are acute.
First, let’s think about an equilateral triangle. An equilateral triangle is a triangle where all three sides are the same length. And because all three sides are the same length, all three angles have the same measure. We could say they all measure 𝑥 degrees. We also know that, in every triangle, the three angles must add up to 180 degrees. 𝑥 plus 𝑥 plus 𝑥 must equal 180 degrees. That’s the same thing as saying three 𝑥 must equal 180 degrees.
To find out what that missing angle is, we need to divide 180 degrees by three. When we do that, we find out that 𝑥 equals 60 degrees. Every angle inside an equilateral triangle is equal to 60 degrees. We know that acute angles measure less than 90 degrees. All three of the angles inside this equilateral triangle are less than 90 degrees. And that means they’re all acute.
The statement “the angles of the equilateral triangle are acute” is true.