Question

let x and y be the following sets: x = {the measures of the three angles of an isosceles triangle} y = {the measures of the three angles of an isosceles triangle with a vertex angle that equals 40 degrees} x∪y {40, 40, 40, 60, 60, 60, 70} {40, 60, 70, 140} {60, 60, 60, 40} {40, 60, 70}

Explanation:

Step1: Recall angle - sum property and triangle angle measures

The sum of the interior angles of a triangle is 180 degrees. For an equilateral triangle, each angle is 60 degrees, so \(Y=\{60,60,60\}\). For an isosceles triangle with a vertex - angle of 40 degrees, the base - angles are \(\frac{180 - 40}{2}=70\) degrees. So the set of angle measures is \(\{40,70,70\}\). The set \(X\) contains all possible angle - measures of isosceles triangles.

Step2: Find the union of sets \(X\) and \(Y\)

The union \(X\cup Y\) is the set of all elements that are in \(X\) or in \(Y\) (or in both). The distinct angle - measures from the angle - measure sets of the given isosceles and equilateral triangles are 40, 60, 70.

Answer:

\(\{40,60,70\}\)