Segment DM is bisector of triangle CDE. A straight line is drawn through point M, parallel to side СD and intersecting side DE

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

By condition, we are given the parallelism of the side CD and the straight line MN. That is, we can say that these are two straight lines intersected by the secant DE. From this we start. We are given the bisector of the CDE angle. If the entire angle is CDE = 68 degrees, then one knot of the corners of our NDM triangle – the angle MDN will be 68: 2. We get one of the corners of the triangle. Angle MDN = 34 degrees. We have already said that straight CD and MN are parallel with DE secant. Then our 68-degree angle will be an inner one-sided angle MND. And by the property we know that if the straight lines are parallel, then the sum of the internal one-sided = 180 degrees. This way we can find the angle MND. 180-68 = 112 degrees. Well, it remains to find one corner of the DMN. Knowing that the sum of the angles of a triangle = 180, then: 180- (34 + 112) = 34 °.