Question

student belcher, cash
properties of parallelograms
solve for the unknown
variable (x).
answer: round to whatever you
see in the problem.

Explanation:

Step1: Use property of parallelogram

In a parallelogram, opposite sides are equal. Also, consecutive angles are supplementary. But here, we use the property that in a parallelogram \(UT = VS\). And since \(UT = 3x + 9\) and \(VS\) (assuming from the angle - side relation in a parallelogram, if we consider the side opposite to the \(45^{\circ}\) angle in a parallelogram - like a rhombus - adjacent sides are equal in a parallelogram. Wait, no, correct property: In a parallelogram \(UT\parallel VS\) and \(UV\parallel TS\). Also, \(UT = VS\). If we assume \(UT = VS\) and from the figure (assuming standard parallelogram side - angle relation where \(3x+9 = 45\))

Step2: Solve the equation

Set up the equation \(3x+9 = 45\). Subtract 9 from both sides: \(3x=45 - 9\). So \(3x = 36\). Divide both sides by 3: \(x=\frac{36}{3}=12\)

Answer:

12