The question asks:

"Find the measure of all the angles of an equilateral triangle."

Solution:

An equilateral triangle is a triangle where all three sides are of equal length. One key property of an equilateral triangle is that all of its interior angles are equal.

1. The sum of the interior angles of any triangle is 180°.
2. Since all three angles of an equilateral triangle are equal, each angle can be calculated by dividing 180° by 3:

$\text{Each angle} = \frac{180^\circ}{3} = 60^\circ$

Thus, all the angles in an equilateral triangle measure 60°.

Let me know if you'd like further explanation! Here are related questions to deepen your understanding:

1. What are the properties of an equilateral triangle aside from angle measures?
2. How does an equilateral triangle differ from an isosceles triangle?
3. Can an equilateral triangle have angles other than 60°? Why or why not?
4. What happens to the angles if the triangle is not planar (e.g., on a sphere)?
5. How do you calculate the height of an equilateral triangle if the side length is known?

Tip: Remember that in an equilateral triangle, the angles and sides are always equal, making it one of the most symmetrical shapes in geometry!