Applying the trapezoid midsegment theorem, the value of z is: 33.
What is the Trapezoid Mid-segment Theorem?
The trapezoid midsegment theorem states that the length of the midsegment of a trapezoid equals the length average of the two bases of the trapezoid.
Thus:
TW = 1/2(XY + UV)
Substitute
3z - 41 = 1/2[(-z + 80) + (4z - 63)]
2(3z - 41) = (-z + 80) + (4z - 63)
6z - 82 = -z + 80 + 4z - 63
Combine like terms
6z - 82 = 3z + 17
6z - 3z = 82 + 17
3z = 99
z = 33
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