4 A uniform T-shaped lamina is formed by rigidly joining two rectangles \(A B C H\) and \(D E F G\), as shown in the diagram.
\includegraphics[max width=\textwidth, alt={}, center]{480a817d-074f-440d-829e-c8f8a9746151-4_748_652_456_644}
- Show that the centre of mass of the lamina is 26 cm from the edge \(A B\).
- Explain why the centre of mass of the lamina is 5 cm from the edge \(G F\).
- The point \(X\) is on the edge \(A B\) and is 7 cm from \(A\), as shown in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{480a817d-074f-440d-829e-c8f8a9746151-4_697_534_1576_753}
The lamina is freely suspended from \(X\) and hangs in equilibrium.
Find the angle between the edge \(A B\) and the vertical, giving your answer to the nearest degree.
(4 marks)