5th Balkan Mathematical Olympiad Problems 1988

5th Balkan Mathematical Olympiad Problems 1988A1.  ABC is a triangle area 1. AH is an altitude, M is the midpoint of BC and K is the point where the angle bisector at A meets the segment BC. The area of the triangle AHM is 1/4 and the area of AKM is 1 - (√3)/2. Find the angles of the triangle.