Answer:
Step-by-step explanation:
The markings on the figure show this to be a parallelogram. That means opposite sides are congruent. Because the sides are parallel, "alternate interior" angles are also congruent.
__
Angle y forms a linear pair with the one marked 83°, so is supplementary to it:
y = 180°-83° = 97°
__
The angle marked y is an exterior angle to the triangle containing the angle marked (7x -5)°. As such, it is equal to the sum of the remote interior angles, the one marked (7x -5)° and the unmarked one that is congruent to (3x +32)°.
(7x -5) +(3x +32) = 97 . . . . . angle relations in the left-side triangle
10x +27 = 97 . . . . . . . collect terms
10x = 70 . . . . . . . . subtract 27
x = 7 . . . . . . . . divide by 10
__
The side marked Z is congruent to the opposite parallel side, so ...
z = 19
__
The missing measures are ...
_____
<em>Additional comment</em>
You can also find the value of y by adding up the interior angles of the right-side triangle. The one not shown there is "alternate interior" to the one marked (7x -5)°, hence has the same measure. This gives ...
(7x -5) +(3x +32) +83 = 180
Subtracting 83° from both sides gives the equation we used above.
