Question

note: angles not necessarily drawn to scale.

$x = square$

Explanation:

Step1: Use vertical angles and right - angle properties

We know that \(\angle CG E\) and \(\angle DGF\) are vertical angles (equal). Also, \(\angle AGC = 90^{\circ}\).

Step2: Calculate \(x\)

Since \(x+\angle DGF=90^{\circ}\) and \(\angle DGF = 23^{\circ}\) (vertical angles), then \(x = 90 - 23\).

Answer:

\(67\)