Question

suppose m is the midpoint of (overline{fg}). find the missing measure. (mg = 7x - 15), (fg = 33) (x = square)

Explanation:

Step1: Recall midpoint property

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

Step2: Substitute given values

We know \( FG = 33 \) and \( MG = 7x - 15 \), so substitute into the equation: \( 33 = 2(7x - 15) \).

Step3: Solve for \( x \)

First, divide both sides by 2: \( \frac{33}{2}=7x - 15 \), which is \( 16.5 = 7x - 15 \). Then add 15 to both sides: \( 16.5 + 15 = 7x \), so \( 31.5 = 7x \). Finally, divide both sides by 7: \( x=\frac{31.5}{7}=4.5 \).

Answer:

\( 4.5 \)