Final answer:
The values of the unknowns x, y, z in the parallelogram RUNS are x = 120°, y = 60°, and z = 60°, because opposite angles are equal and consecutive angles are supplementary (add up to 180°).
Step-by-step explanation:
The question involves finding the unknown angles in a parallelogram. In a parallelogram, opposite angles are equal, and consecutive angles are supplementary, meaning they add up to 180°. Let's denote the angles at vertices R, U, N, and S as R, U, N, and S respectively. If we call the angle at vertex U 'x', then angle S is also 'x' since they are opposite angles. Likewise, if angle R is 'y', then angle N is also 'y'. Since U and R are consecutive angles, U + R = 180° or x + y = 180°. We know one angle (let's say angle S, which is 'x') is 120°, therefore angle R (which is 'y') is 60° because they are supplementary. Consequently, using the same reasoning, angle U (which is 'x') also equals 120° and angle N (which is 'y') equals 60°.
If 'z' represents the measure of any internal angle of the parallelogram, it takes either the value of 'x' or 'y' because there are only two distinct internal angles in a parallelogram. Therefore, 'z' could be 120° or 60° corresponding to the measures of 'x' and 'y' respectively.
So, the correct answer is B) x = 120°, y = 60°, z = 60°.