The segment DM is the bisector of the triangle CDE through point M, a straight line is drawn parallel to the side CD and intersecting the side DM at point I. find the angles of the triangle DMI if the angle CDE = 68 degrees
Since, by condition, the segment DM is the bisector of the angle CDE, then the angle CDM = EDM = CDE / 2 = 68/2 = 34.
The MH segment is parallel to the CD side of the triangle, the DM is a secant intersecting two parallel lines.
Then the angle DМН = СDМ as criss-crossing angles at the intersection of parallel secant lines.
Angle DMH = CDM = 34.
Consider a triangle DМН. The sum of its internal angles is 180, then the angle DHM = (180 – 34 – 34) = 112.
Answer: The angles of the triangle DHM are 34, 34, 112.
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