Question

question
in the figure above, what is the average (arithmetic mean) of w, x, y, and z?
90
100
120
it cannot be determined from the information given.

Explanation:

Step1: Recall angle properties

Vertical angles are equal, and linear pairs are supplementary (sum to \(180^\circ\)). So \(x + y = 180\) (linear pair), \(w + z = 180\) (linear pair), or we can also note that around a point, the sum of angles is \(360^\circ\), so \(x + y + w + z = 360\).

Step2: Calculate the average

The arithmetic mean of \(w, x, y, z\) is \(\frac{w + x + y + z}{4}\). Substitute \(w + x + y + z = 360\) into the formula: \(\frac{360}{4}=90\).

Answer:

90