Answer:
x = 8
z = 15
y = 118°
Explanation:
First, we know that these are similar. That means that if we know which angles correspond to each other, those are equal, and the sides that correspond to each other have a common ratio. I went ahead and rotated PQRS so that it visually aligns with WXYZ -- that image is attached. We can do this because similar shapes must have the same angles, so aligning the angles works here. Using that, we can see that, based on the angles, QR matches up with XY, WZ matches up with PS, and so on.
We can then say that there is a common ratio between the corresponding sides.
WZ/PS = XW/PQ = ZY/RS = 9/6 = 12/x = z/10
9/6 simplifies to 3/2, so we have
3/2 = 12/x
multiply both sides by x to no longer have it as a denominator
3 * x / 2 = 12
multiply both sides by 2 and divide both sides by 3 to isolate x
x = 8
3/2 = z / 10
multiply both sides by 10 to isolate z
z = 15
In the corresponding figures, we can see that y matches up with ∠WXY. Thus, the two angles are equal and y = 118°