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

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

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

Answer

Explanation:

Step1: Use opposite - sides 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 the equation 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: Find the lengths of the sides

If $n = 10$:

  • $CF=6n-1=6\times10-1=59$.
  • $FE=4n + 2=4\times10+2=42$.
  • $CD=5n + 9=5\times10+9=59$.

Answer:

$n = 10$, $CF = 59$, $FE = 42$