Applying similar polygon, the required parts are
x = 8
y = 118 degrees
z = 15
How to find the required parts
The parts are sought using the knowledge of similar polygons. The image is arranged to look alike so that the corresponding part is easily spotted
In the figure, the proportion used to solve for x is
12 / x = 9/6
9x = 12 * 6
x = 72 / 9
x = 8
The corresponding angles are equal. So , y = 118 degrees
Solving for z
z/10 = 9/6
z = 10 * 9 / 6
z = 15