Final answer:
Upon calculating the measurements of the angles in the triangle, we find that m∠x = 55 degrees, m∠y = 13 degrees, and m∠z = 102 degrees. The angle representing the remote exterior angle is the smallest of the non-adjacent interior angles to the largest angle, which in this case is m∠y = 13 degrees, option C.
Step-by-step explanation:
The goal is to determine which of the given angles represents the remote exterior angle of a triangle. According to the angle sum property of a triangle, the sum of the angles equals 180 degrees. We are given:
- m∠x = 4n - 18
- m∠y = n + 8
- m∠z = 133 - 6n
By adding the three angles together and equating to 180 degrees, we get the equation:
4n - 18 + n + 8 + 133 - 6n = 180. Simplifying this, we have -5n + 123 = 180, and solving for 'n' gives us n = -57/5. Substituting this value into the angles' expressions, we can find their measures:
- m∠x = 4(-57/5) - 18
- m∠y = (-57/5) + 8
- m∠z = 133 - 6(-57/5)
The calculations yield m∠x = 55, m∠y = 13, and m∠z = 102 degrees, respectively. By analyzing the values, we can see that m∠z = 102 degrees cannot be the remote exterior angle because it is an interior angle. m∠x and m∠y are the non-adjacent interior angles to m∠z, and since m∠y is the smallest, it is the angle remote to the largest interior angle m∠z. Thus, the correct answer would be m∠y = 13 degrees, represented by option C.