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In the diagram below of triangle NPQ, R is a midpoint of NP and S is a midpoint of PQ. If RS = 23 - x, and NQ = 2x + 18, what is the measure of NQ?

In The Diagram Below Of Triangle NPQ R Is A Midpoint Of NP And S Is A Midpoint Of PQ If RS 23 X And NQ 2x 18 What Is The Measure Of NQ class=

Sagot :

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.

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