Line segment AD is the bisector of triangle ABC. A line is drawn through point D, parallel to side AB and intersecting side AC

Line segment AD is the bisector of triangle ABC. A line is drawn through point D, parallel to side AB and intersecting side AC at point F. Find the angles of triangle ADF if the angle BAC = 72 degrees.

If AD is a bisector, then half of the angle BAC = 36 degrees. We found one corner. Further. Sections AB and DF are parallel with secant AC, and the one-sided angles add up to 180 degrees. Corner BAC and DAF int. one-sided. 180-72 = 108-angle DFA. It remains to find the last angle by the sum of the angles of the triangle. Angle ADF = 180- (36 + 108) = 36 degrees. The triangle turned out to be isosceles)