Question

ux is the midsegment of the trapezoid stvw. if vw = -y + 82, ux = y, and st = y + 8, what is the value of y? y =

Explanation:

Step1: Recall the midsegment theorem for trapezoids.

The midsegment of a trapezoid is the average of the two bases. So, \( UX=\frac{ST + VW}{2} \).

Step2: Substitute the given expressions into the formula.

We know \( UX = y \), \( ST=y + 8 \), and \( VW=-y + 82 \). Substituting these into the formula gives:
\( y=\frac{(y + 8)+(-y + 82)}{2} \)

Step3: Simplify the right - hand side of the equation.

First, simplify the numerator: \( (y + 8)+(-y + 82)=y + 8 - y+82=90 \).
So the equation becomes \( y=\frac{90}{2} \)

Step4: Solve for y.

\( \frac{90}{2}=45 \), so \( y = 45 \).

Answer:

\( 45 \)