Question

1. look at the figure, ▱fgme. find the length of $overline{gm}$. 15 25 10 20

Explanation:

Step1: Use property of parallelogram

In parallelogram FGME, opposite - sides are equal. So, $FM = GE$ and $FG = EM$. We can set up an equation using the fact that opposite - sides are equal. Let's assume we use the equality of the non - parallel sides (if we consider the given expressions). We know that the opposite sides of a parallelogram are equal. So, $7x−1=6x + 2$.

Step2: Solve the equation for x

Subtract $6x$ from both sides of the equation $7x−1=6x + 2$. We get $7x-6x-1=6x-6x + 2$, which simplifies to $x-1=2$. Then add 1 to both sides: $x=2 + 1=3$.

Step3: Find the length of $\overline{GM}$

The length of $\overline{GM}$ is given by the expression $2x + 4$. Substitute $x = 3$ into the expression $2x+4$. We have $2\times3+4=6 + 4=10$.

Answer:

10