Question

1. find wx.

s -----> t with length 10x + 5
w -----> x with length 7x + 8
u -----> (a point) with length 8x - 1
(the figure appears to be a trapezoid or a similar figure with markings indicating midsegments or congruent segments on the non-parallel sides.)

Explanation:

Step1: Identify the theorem

This is a trapezoid with a midline (or midsegment) \( WX \). The Midline Theorem for trapezoids states that the length of the midline is the average of the lengths of the two bases. So, \( WX=\frac{ST + U V}{2} \)? Wait, no, looking at the diagram, \( ST = 10x + 5 \), \( UV=8x - 1 \), and \( WX = 7x + 8 \). Wait, actually, in a trapezoid, the midsegment (the segment connecting the midpoints of the non - parallel sides) is equal to the average of the two parallel sides. So here, \( WX \) is the midsegment, so \( WX=\frac{ST + UV}{2} \)

Step2: Set up the equation

Substitute the expressions: \( 7x + 8=\frac{(10x + 5)+(8x - 1)}{2} \)

Step3: Simplify the right - hand side

First, simplify the numerator: \( (10x + 5)+(8x - 1)=10x+8x + 5 - 1=18x + 4 \)
Then, the right - hand side becomes \( \frac{18x + 4}{2}=9x+2 \)

Step4: Solve for x

Now we have the equation \( 7x + 8=9x + 2 \)
Subtract \( 7x \) from both sides: \( 8 = 2x+2 \)
Subtract 2 from both sides: \( 6 = 2x \)
Divide both sides by 2: \( x = 3 \)

Step5: Find the length of WX

Substitute \( x = 3 \) into the expression for \( WX \): \( WX=7x + 8 \)
\( WX=7\times3+8=21 + 8=29 \)

Answer:

\( 29 \)