Question

break!
week
streak
note: angles not necessarily drawn to scale.

Explanation:

Step1: Use vertical angles and right - angle properties

Since \(AB\perp CD\) at \(G\), \(\angle CGD = 90^{\circ}\). The angle between \(EF\) and \(CD\) is \(22^{\circ}\). Also, \(\angle EGB=x^{\circ}\).
We know that the sum of angles around a point on a straight line is \(180^{\circ}\). But using the property of vertical angles and right - angle: \(x + 90+22=180\) (because \(AB\) is a straight line, \(\angle AGB = 180^{\circ}\), and \(\angle AGC = 90^{\circ}\)).

Step2: Solve the equation for \(x\)

$$
LATEXBLOCK0
$$

Answer:

\(68\)