Question

suppose m is the midpoint of \\( \overline { f g } \\). find the missing measure. \\( m g = 7 x - 15, f g = 33 \\) \\( x = \\)

Explanation:

Step1: Use the midpoint property

Since \(M\) is the midpoint of \(\overline{FG}\), then \(MG=\frac{1}{2}FG\).

Step2: Substitute the given values

Given \(MG = 7x - 15\) and \(FG = 33\), substitute into the equation \(7x-15=\frac{1}{2}\times33\).
Simplify the right - hand side: \(\frac{1}{2}\times33 = 16.5\). So the equation becomes \(7x-15 = 16.5\).

Step3: Solve for \(x\)

Add \(15\) to both sides of the equation: \(7x=16.5 + 15\).
\(7x=31.5\).
Divide both sides by \(7\): \(x=\frac{31.5}{7}\).
\(x = 4.5\).

Answer:

\(4.5\)