<image>As shown in the figure, in the parallelogram \(ABCD\), an arc is drawn with center \(A\) and radius equal to the length of \(AB\), intersecting \(AD\) at point \(F\). Then, arcs are drawn with centers at points \(B\) and \(F\) with radius greater than \(\frac{1}{2} BF\), intersecting at point \(P\). Segment \(AP\) is extended to intersect \(BC\) at point \(E\). Connect \(EF\) and \(AE\), and \(BF\) intersects these segments at point \(O\). If the perimeter of quadrilateral \(ABEF\) is 40 and \(BF = 10\), find \(\angle ABC =\) _____.
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