Final answer:
Without a diagram or additional context, it's impossible to determine the precise relationships between the angles marked as x, y, and z compared to angle w, which is given as 61.1 degrees. If we assume a triangle, it's plausible that x and z are congruent to w and y is a supplementary angle, leading to a value of 3.3 degrees for the expression x+z−y.
Step-by-step explanation:
If the angle marked with w is 61.1 degrees, and the question implies a geometric relationship between angles w, x, y, and z, we can proceed to find the measures of the angles marked as x, y, and z. However, without additional information or a diagram, it is impossible to determine the relationships between these angles. If it is a triangle and w is an angle in that triangle, then we could use the fact that the angles in a triangle sum up to 180 degrees to find the other angles. Without this context, we're left with multiple choices provided in the question. If we assume the context of a triangle, answer (b) x=61.1, y=61.1, z=61.1 would not be consistent with the triangle angle sum theorem unless it's an equilateral triangle. Answer (a) x=61.1, y=180−61.1, z=61.1 could be valid if x and z are also angles in the triangle and y is an exterior angle, which would then make y the supplementary angle to w. With assumptions and given choices, the best we can deduce is that x and z are likely congruent to w, and y is the supplementary angle to these. Thus, answer (a) is most plausible if we are referring to a triangle with w as an interior angle and y as an exterior angle.
To calculate x+z−y, using answer (a) we would get: x + z - y = 61.1 + 61.1 - (180 - 61.1) = 122.2 - 118.9 = 3.3 degrees.