Question

what value of x will make ab perpendicular to cd?

Explanation:

Step1: Recall perpendicular - angle property

If \(AB\perp CD\), then the angle formed at the intersection (e.g., \(\angle CGB\)) is \(90^{\circ}\). So, \(18+(11x - 5)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(18+(11x - 5)=11x+(18 - 5)=11x + 13\). So, the equation becomes \(11x+13 = 90\).

Step3: Solve for \(x\)

Subtract 13 from both sides: \(11x=90 - 13\), so \(11x=77\). Then divide both sides by 11: \(x=\frac{77}{11}=7\).

Answer:

\(7\)