A Strange Star in a Strange Shape

Geometry Level 3

A strange shape can be made by joining two semi-ellipses with same major axis, but different minor axes. The above image is an example of one such shape. The blue region is a semi-ellipse with semi-minor axis \((OA)\) of length \(3\). The pink region is a semi-ellipse with semi-minor axis \((OE)\) of length \(4\). The major axis \((GC)\), common to both semi-ellipses has a length of \(10\).

Now, a \(7\) - pointed star in inscribed in this strange shape, symmetric about line \(AE\), such that \(BH\) is parallel to major axis, \(\angle H = 90^{\circ}\), and line \(GC\) bisects angles \(\angle C\) and \(\angle G\).

Calculate \(\angle A + \angle B + \angle C + \angle D + \angle F + \angle G + \angle H\).

Give your answer in degrees.

This problem is a part of the set - A Strange Shape

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