Geometry · Angle chasing · Isosceles triangles · Circumcentre · Inscribed angle theorem · 30 60 90 triangle
In a triangle \(ABC\) we have \(\angle ABC = 45^\circ\) and \(\angle CAB = 15^\circ\). Let \(M\) be the point of the ray \(BC\) for which
\[ \overrightarrow{BM} = 3 \cdot \overrightarrow{BC} . \]
Determine the angles of the triangle \(ABM\).
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Serbian National Competition (Drzavno takmicenje) 2008, high school grade I, category A, problem 2. Organized by the Mathematical Society of Serbia (DMS). Source