# The segment DM is the bisector of the triangle CDE. Through point M, a straight line is drawn intersecting side De to point N.

July 28, 2021 | education

| **The segment DM is the bisector of the triangle CDE. Through point M, a straight line is drawn intersecting side De to point N. so that DN = MN Set the angles of the triangle DMN if the angle CDE = 74 degrees.**

To solve the problem, consider the figure.

Since the segment DM is the bisector of the angle CDE, the angle MDN = CDE / 2 = 74/2 = 37.

Consider a triangle MDN, for which, by condition, MN = DN.

Since MN = DN, then MDN is an isosceles triangle, in which the angles at the base are equal, therefore, the angle DMN = MDN = 37.

Then the angle MND at the vertex is equal to:

MND = 180 – 2 * 37 = 106.

Answer: The angles of triangle DMN are 37, 37 and 106.

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