Question

solve for x.

x =

Explanation:

Step1: Use the property of corresponding angles

Since \(CD\parallel EF\), \(\angle AGD\) and \(\angle EHB\) are corresponding angles. And \(\angle AGD=(85 - 2x)^{\circ}\), \(\angle EHB=(93 - 4x)^{\circ}\). Corresponding angles are equal, so \(85-2x = 93 - 4x\).

Step2: Solve the equation for \(x\)

Add \(4x\) to both sides of the equation: \(85-2x + 4x=93 - 4x+4x\), which simplifies to \(85 + 2x=93\).
Subtract \(85\) from both sides: \(2x=93 - 85\), so \(2x = 8\).
Divide both sides by \(2\): \(x=\frac{8}{2}\).

Answer:

\(x = 4\)