Answer:
The measure of NQ is 32 units.
Explanation:
Given that R is a midpoint of NP and S is a midpoint of PQ, the by the Midpoint Theorem for Triangles, we have:
[tex]RS=\frac{1}{2}\times NQ[/tex]
Substituting the given expressions, we have:
[tex]\begin{gathered} 23-x=\frac{1}{2}(2x+18) \\ 2(23-x)=2x+18 \end{gathered}[/tex]
Next, solve for x:
[tex]\begin{gathered} 46-2x=2x+18 \\ 46-18=2x+2x \\ 28=4x \\ x=\frac{28}{4} \\ x=7 \end{gathered}[/tex]
Thus, the measure of NQ will then be:
[tex]\begin{gathered} NQ=2x+18 \\ =2(7)+18 \\ =14+18 \\ =32\text{ units} \end{gathered}[/tex]
The measure of NQ is 32 units.
