Question

given parallelogram defg below, eh = 57. if hg = -x + 1, solve for x.

Explanation:

Step1: Use property of parallelogram diagonals

In a parallelogram, diagonals bisect each other. So \(EH = HG\).

Step2: Set up the equation

Since \(EH = 57\) and \(HG=-x + 1\), we have \(57=-x + 1\).

Step3: Solve for \(x\)

Subtract \(1\) from both sides: \(57-1=-x\), so \(56=-x\). Multiply both sides by \(- 1\): \(x=-56\).

Answer:

\(x = - 56\)