Question

x and u are the midpoints of the legs, $overline{wy}$ and $overline{tv}$, of trapezoid tvwy. if ty = 46 and vw = 70, what is ux?

Explanation:

Step1: Recall mid - segment formula

The length of the mid - segment of a trapezoid (the line segment connecting the mid - points of the non - parallel sides) is given by the formula $UX=\frac{TY + VW}{2}$, where $TY$ and $VW$ are the lengths of the parallel sides of the trapezoid.

Step2: Substitute given values

We are given that $TY = 46$ and $VW=70$. Substitute these values into the formula: $UX=\frac{46 + 70}{2}$.

Step3: Calculate the result

First, add the numbers in the numerator: $46+70 = 116$. Then, divide by 2: $\frac{116}{2}=58$.

Answer:

58