Segment DM – bisector of triangle ADC. A straight line is drawn through point M, parallel to side CD

Segment DM – bisector of triangle ADC. A straight line is drawn through point M, parallel to side CD and intersecting side DA at point N. Find the angles of the triangles DMN if the angle ADC = 72 °

Consider the triangle DMN. In it, the angle NDM = 72 °: 2 = 36 °, since the angle ADC = 72 ° in the triangle ADC, and the segment DM is the bisector of the angle ADC (by condition), hence the angle MDC = 36 °. The angle DMN is equal to the angle MDС, as are the internal cross-lying angles at DС || MN and secant DM, since it is known from the condition that a straight line is drawn through the point M, parallel to the side CD and intersecting the side DA at point N. Since the sum of the angles in the triangle is 180 °, you can find the third angle of the triangle DMN. Angle MND = 180 ° – (36 ° + 36 °) = 108 °.
Answer: 36 °; 36 °; 108 ° are the corners of the DMN triangle.