Answer: 27°
Step-by-step explanation:
The easiest way to find the measure of angle Z is to know that in a rhombus, the diagonals are perpendicular bisectors of each other. This means that all the four angles in the center are 90°.
Since we know that all angles in a triangle add up to 180°, we can set the sum of z, 63, and 90 to be 180 and solve for z.
[tex]z+63+90=180\\z+153=180\\z=27[/tex]
Hence, z is 27°.
