Question

what is the value of z?

Explanation:

Step1: Recall the total angle around a point

The sum of angles around a point is \(360^{\circ}\). But here, we can also use the fact that the sum of angles in a set of adjacent angles (if we consider the right - angle - like situation). Wait, another approach: the sum of angles in a circle - like arrangement (but here it's a straight - line - related concept in a more complex angle setup). Let's use the fact that \(z + 93^{\circ}+36^{\circ}+90^{\circ}=360^{\circ}\) (assuming the vertical line is perpendicular to the left - most line in a full - circle sense). Wait, no, actually, if we consider the fact that \(z+93^{\circ}+36^{\circ}= 180^{\circ}\) (because they form a linear pair with the right - angle - like part? No, wait, another way. Let's use the property of angles around a point. But if we assume that the two non - labeled angles (the right - angle - like one and the other) are part of a \(360^{\circ}\) sum. Wait, no, actually, if we consider the fact that \(z + 93^{\circ}+36^{\circ}=180^{\circ}\) (because they are adjacent angles on a straight line).

$$z+93 + 36=180$$

Step2: Solve for \(z\)

Subtract \(93 + 36\) from both sides.

$$z=180-(93 + 36)$$

$$z=180 - 129$$

$$z = 51$$

Answer:

\(51\)