What is the measure of ∠DFE? What sort of triangle is ∆DEF?
From the picture, we can see that the three sides of the triangle, DF, FE, and ED are all congruent and therefore have the same length. All the angles are congruent as well. That makes ∆DEF an equilateral triangle.
How can we figure out the angles of an equilateral triangle? Spoiler alert: They're all equal. We'll call each angle measurement x. Since they're all equal and we know all of a triangle's angles add up to 180°, we can set up this equation.
x + x + x = 3x = 180 x = 60
In other words, all the angles in an equilateral triangle have measurements of 60°, including our dear ∠DFE.