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 the property of parallelogram

In a parallelogram, opposite sides are equal. So, \(CF = DE\) and \(CD=FE\).
For \(CF = DE\), we have \(6n - 1=5n + 9\).

Step2: Solve the equation \(6n - 1=5n + 9\)

Subtract \(5n\) from both sides: \(6n-5n-1 = 5n - 5n+9\), which gives \(n-1=9\).
Add \(1\) to both sides: \(n-1 + 1=9 + 1\), so \(n = 10\).

Step3: Calculate the lengths of the sides

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

Answer:

\(n = 10\), \(CF = 59\), \(FE = 42\)