Question

what is the value of z?

Explanation:

Step1: Recall angle - sum property of a right - angled system

Assume the angles are part of a system where the sum of angles around a point is 360° or in a right - angled related context. If we assume the vertical and horizontal lines are perpendicular (90° angles), and we want to find the remaining angle $z$. The sum of the given angles and $z$ in a 90° related context should equal 90°.

Step2: Calculate the value of $z$

We know that the sum of the two given angles and $z$ is 90°. Let's calculate $z$ as $z = 90-(55.4 + 38.9)$. First, add the two given angles: $55.4+38.9 = 94.3$. But this is wrong as we assume a 90 - degree context. Let's assume the angles are part of a 360 - degree system. The sum of the three angles is 360°. So $z=360-(90 + 55.4+38.9)$. First, add the non - $z$ angles: $90 + 55.4+38.9=184.3$. Then $z = 360 - 184.3$.
$z=175.7$

Answer:

$175.7$