find the angle of a suspended lamina, check the photo for the full question

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Centre of mass related question

I don't understand how to tackle this question, I know how to find the centre of mass of the shape but don't know what is the next step.

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Draw a line from the COM coordinates you found to point C in the diagram. This line makes an angle with the horizontal a point C (call the angle $\theta$). If you took a compass and drew a circle with the radius extending from point C to the COM coordinates, the bottom of the circle would be the minimum potential energy. The angle it makes with the vertical is just $\frac{\pi}{2}+\theta$