Question

find ( mangle u ) in rhombus ( tuvw ).

Explanation:

Step1: Use rhombus consecutive angles property

Consecutive angles in a rhombus are supplementary, so:
$$(x+36) + 8x = 180$$

Step2: Simplify and solve for $x$

Combine like terms and isolate $x$:
$$9x + 36 = 180$$
$$9x = 180 - 36$$
$$9x = 144$$
$$x = \frac{144}{9} = 16$$

Step3: Find $m\angle W$

Substitute $x=16$ into $8x$:
$$m\angle W = 8(16) = 128^\circ$$

Step4: Use rhombus opposite angles property

Opposite angles in a rhombus are equal, so $m\angle U = m\angle W$.

Answer:

$128$