Question

figure cdef is a parallelogram. which equations are correct? select three options. n = 10 n = 7 cf = 59 fe = 42 cd = 30

Explanation:

Step1: Recall property of parallelogram

In a parallelogram, opposite - sides are equal. So, $CF = DE$ and $CD = FE$. Let's assume $CF = 6n - 1$ and $DE = 5n+9$, then $6n - 1=5n + 9$.

Step2: Solve for n

Subtract $5n$ from both sides of the equation $6n - 1=5n + 9$. We get $6n-5n-1=5n - 5n+9$, which simplifies to $n-1 = 9$. Then add 1 to both sides: $n=9 + 1=10$.

Step3: Calculate side - lengths

If $n = 10$, then $CF=6n - 1=6\times10-1=59$.
$FE=CD = 4n + 2=4\times10+2=42$.
$CD=4n + 2=42$ and $FE = 42$, $CF = 59$, and $n = 10$.

Answer:

A. $n = 10$
C. $CF = 59$
D. $FE = 42$