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Applying the segment addition theorem, the length of line segment VW is: 2 units.
<h3>What is the Segment Addition Theorem?</h3>The segment addition theorem states that the sum of the lengths of two segments that make up a larger line segment equals the measure of the larger line segment, if the point on the line segments are collinear.
UV = 8x
VW = x+1
UW = 10
UV + VW = UW (segment addition theorem)
Substitute the values
8x + (x + 1) = 10
Open bracket
8x + x + 1 = 10
Combine like terms
9x + 1 = 10
Subtract 1 from both sides
9x + 1 - 1 = 10 - 1
9x = 9
Divide both sides by 9
9x/9 = 9/9
x = 1
VW = 8x + (x + 1)
Plug in the value of x
VW = x + 1
VW = 1 + 1
VW = 2 units.
Therefore, applying the segment addition theorem, the length of line segment VW is: 2 units.
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