From one vertex of the triangle, the median, bisector and height were drawn.

From one vertex of the triangle, the median, bisector and height were drawn. They divided the corresponding corner of the triangle into 4 equal angles. Find the values of all the angles of the triangle.

The solution of the problem:

1) We schematically represent the problem, where:

∆АВС, СМ – median, СО – bisector, СН – height, ∟СНВ = 90о.

2) This condition is satisfied if ∆АСВ is rectangular, then:

AM = MS, ∟A = ∟ACM = 90 °: 4 = 22.5 °;

∟B = 90o – 22.5o = 67.5o.

Answer: the angles of the triangle are equal to: 90o; 22.5 °; 67.5o.