In an isosceles triangle ABC with base AC, the segment BF is the median.

In an isosceles triangle ABC with base AC, the segment BF is the median. Find the degree measures of the angles of triangle BFC if the angle ABC = 40 degrees.

1) Since the triangle ABC is isosceles, AB = BC and BF is the median, then BF is also the height and the bisector. Hence the angle CBF = half of the angle ABC = 40/2 = 20 °.
2) Since BF is the height, then BF is perpendicular to AC, which means that the angle BFC = 90 °.
3) Consider a triangle BCF in which the angle BFC = 90 °, the angle FBC = 20 °. The sum of the angles of a triangle is 180 ° => angle BCF = 180-90-20 = 70 °
Answer: BFC angle = 90 °, FBC angle = 20 °, BCF angle = 70 °.