Question

suppose m is the midpoint of \\(\overline{fg}\\). find the missing measure. \\(fm = 3x - 4\\), \\(mg = 5x - 26\\) \\(fg =\\)

Explanation:

Step1: Use midpoint property

Since M is the midpoint of \(\overline{FG}\), \(FM = MG\). So we set up the equation:
\(3x - 4 = 5x - 26\)

Step2: Solve for x

Subtract \(3x\) from both sides:
\(-4 = 2x - 26\)
Add 26 to both sides:
\(22 = 2x\)
Divide both sides by 2:
\(x = 11\)

Step3: Find FM and MG

First, find \(FM\): \(FM = 3x - 4 = 3(11) - 4 = 33 - 4 = 29\)
Since \(FM = MG\), \(MG = 29\)

Step4: Find FG

\(FG = FM + MG = 29 + 29 = 58\)

Answer:

58