Final answer:
That with three angles already known or given in a triangle, the values can be determined as long as the sum of those angles equals 180 degrees.
a. x = 60 degrees
b. y = 50 degrees
c. z = 70 degrees
d. Cannot be determined from the given information.
Explanation:
In a triangle, the sum of all three interior angles is always 180 degrees. Here, two angles are given: x = 60 degrees and y = 50 degrees. To find the third angle z, subtract the sum of x and y from 180 degrees: z = 180 - (x + y) = 180 - (60 + 50) = 180 - 110 = 70 degrees. Therefore, the values of x, y, and z in the triangle are x = 60 degrees, y = 50 degrees, and z = 70 degrees, respectively.
The angles in any triangle always add up to 180 degrees. Utilizing this fundamental property, we deducted the missing angle z by subtracting the sum of the given angles x and y from 180 degrees. This yields the measure of angle z, completing the determination of all three angles in the triangle. The given information provided concrete angles x and y, enabling us to calculate the missing angle z accurately.
It's important to note that with three angles already known or given in a triangle, the values can be determined as long as the sum of those angles equals 180 degrees. However, if insufficient information or fewer than three angles are provided, determining the specific values becomes impossible without additional data or angles.