Question

w=\underline{\quad}\
x=\underline{\quad}\
y=\underline{\quad}\
z=\underline{\quad}

Explanation:

Step1: Identify vertical angles

Vertical angles are equal. $w$ and the $43^\circ$ angle are not vertical; instead, $w$ forms a right angle pair with $43^\circ$? No, correct: $w + 43^\circ = 90^\circ$? No, wait, the horizontal and vertical lines are perpendicular, so the angle between vertical and horizontal is $90^\circ$.
So $w + 43^\circ = 90^\circ$
$\implies w = 90^\circ - 43^\circ = 47^\circ$

Step2: Find x (vertical to 43°)

$x$ is vertical to $43^\circ$, so $x = 43^\circ$

Step3: Find y (vertical to w)

$y$ is vertical to $w$, so $y = w = 47^\circ$

Step4: Find z (supplementary to x)

$z$ and $x$ are supplementary (linear pair): $z + x = 180^\circ$
$\implies z = 180^\circ - 43^\circ = 137^\circ$

Answer:

$w=47^\circ$, $x=43^\circ$, $y=47^\circ$, $z=137^\circ$