Question

find ( mangle x ) in rhombus ( vwxy ).
( mangle x = square^circ )

Explanation:

Step1: Adjacent angles sum to 180°

In a rhombus, adjacent angles are supplementary. So:
$$(4z + 74) + (6z - 4) = 180$$

Step2: Simplify and solve for z

Combine like terms and isolate z:
$$10z + 70 = 180$$
$$10z = 180 - 70$$
$$10z = 110$$
$$z = \frac{110}{10} = 11$$

Step3: Find $m\angle Y$

Substitute z=11 into $\angle Y$ expression:
$$m\angle Y = 4(11) + 74 = 44 + 74 = 118^\circ$$

Step4: Opposite angles are equal

In a rhombus, opposite angles are congruent, so $m\angle X = m\angle Y$.

Answer:

$118$