Inside an equilateral triangle $ABC$ one constructs points $P, Q$ and $R$ such that \[\angle QAB = \angle PBA = 15^\circ,\\ \angle RBC = \angle QCB = 20^\circ,\\ \angle PCA = \angle RAC = 25^\circ.\] Determine the angles of triangle $PQR.$
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Tags: Triangle, angles, geometry, IMO Shortlist, IMO 1979
Inside an equilateral triangle $ABC$ one constructs points $P, Q$ and $R$ such that \[\angle QAB = \angle PBA = 15^\circ,\\ \angle RBC = \angle QCB = 20^\circ,\\ \angle PCA = \angle RAC = 25^\circ.\] Determine the angles of triangle $PQR.$