W X Y Z is a rhombus. If m

Explanation:

We can use the SSS congruence theorem to prove triangle WZX is congruent to triangle YZX. Then that leads to angle WZX = angle YZX.

In short, we've proven that ZX bisects angle WZY. Similarly, segment WY cuts angle XYZ in half. The proof is the same idea as mentioned in the first paragraph. For any rhombus, the diagonals always bisect the angles inside the rhombus.

Also, for any rhombus, the adjacent angles are supplementary.

So,

(angle WZY) + (angle XYZ) = 180

(angle WZY) + (136) = 180

angle WZY = 180 - 136

angle WZY = 44 degrees

Then we cut this in half to get the measure of angle XZY

angle XZY = (angle WZY)/2

angle XZY = (44)/2

angle XZY = 22 degrees

Set this equal to the 10x-8 expression and solve for x.

10x-8 = 22

10x = 22+8

10x = 30

x = 30/10

x = 3