Question

sv is the midsegment of the trapezoid tuwx. if wx = z - 15, sv = z, and tu = 2z - 61, what is the value of z?

Explanation:

Step1: Recall mid - segment formula

The formula for the length of the mid - segment of a trapezoid is $SV=\frac{WX + TU}{2}$.

Step2: Substitute given values

Substitute $WX = z - 15$, $SV = z$, and $TU = 2z - 61$ into the formula: $z=\frac{(z - 15)+(2z - 61)}{2}$.

Step3: Simplify the right - hand side

First, simplify the numerator: $(z - 15)+(2z - 61)=z - 15+2z - 61 = 3z-76$. So the equation becomes $z=\frac{3z - 76}{2}$.

Step4: Cross - multiply

Multiply both sides of the equation by 2: $2z=3z - 76$.

Step5: Solve for z

Subtract $2z$ from both sides: $0 = 3z-2z - 76$. Then $z = 76$.

Answer:

$76$