Final answer:
The measurement of angle x in an equilateral triangle is 60° and the length of each side is 60 units since all angles in an equilateral triangle are equal and the total adds up to 180°.
Step-by-step explanation:
The measurement of angle x and each side of an equilateral triangle is: a) x = 60°, Each side = 60 units. In an equilateral triangle, all sides are equal in length and all interior angles are equal. Since the sum of the angles of any triangle is 180°, each angle in an equilateral triangle measures 60°.
Using the Pythagorean theorem, which states that in a right triangle, the sum of the squares of the lengths of the two legs is equal to the square of the length of the hypotenuse (a² + b² = c²), we can explore geometric principles that apply to different shapes and scenarios. However, because we're dealing with an equilateral triangle, there is no direct use of the Pythagorean theorem in this context as all sides and angles are identical.
To find the value of x and the measure of each side of an equilateral triangle, we need to know a particular side length or angle measurement. Unfortunately, the given options do not provide enough information to determine the values. In an equilateral triangle, all angles are 60 degrees and all sides are equal in length. So, if we are given the length of a side, we can find the value of x which would be equal to 60 degrees. However, without knowing any specific measurements, we cannot determine the values.