The segment DM is the bisector of the triangle CDE. A straight line is drawn through point M, parallel to the side CD

The segment DM is the bisector of the triangle CDE. A straight line is drawn through point M, parallel to the side CD and intersecting the side DE at point N. Find the angles of the triangle DMN if the angle CDE = 68.

Since the segment DM is the bisector of the angle CDE, the angle CDM = EDM = CDE / 2 = 68/2 = 34.

According to the condition, the segment МН is parallel to the side СD, then the secant line DМ intersects two parallel lines СD and МН, and therefore, the cross-lying angles СDМ and DМН are equal.

Angle DMH = CDM = 34.

Then, in the triangle DМН, the angle DНМ = (180 – 34 – 34) = 112.

Answer: The angles of the triangle DMH are 34, 34, 112.