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: Use opposite - sides property of parallelogram

In a parallelogram, opposite sides are equal. So, $CF = DE$ and $CD=FE$. That is, $6n - 1=5n + 9$ and $4n + 2=FE$.

Step2: Solve the equation $6n - 1=5n + 9$ for $n$

Subtract $5n$ from both sides: $6n-5n-1=5n - 5n+9$, which gives $n - 1=9$. Then add 1 to both sides: $n=9 + 1=10$.

Step3: Find the lengths of the sides

If $n = 10$, then $CF=6n-1=6\times10 - 1=59$.
$FE=4n + 2=4\times10+2=42$.
$CD = 4n + 2=4\times10+2=42
eq30$.

Answer:

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