The angle at the vertex B of the rhombus ABCD is 170 degrees. Points M and H are the bases

| September 25, 2021 | education

The angle at the vertex B of the rhombus ABCD is 170 degrees. Points M and H are the bases of the perpendiculars lowered from the top A to the straight lines: BC and CD. Find the angles of the triangle AMН.

The sum of the adjacent angles of the rhombus is 180, then the angle BAD = 180 – 170 = 10.

The opposite angles of the rhombus are equal to each other, then the angle ВСD = BAD = 10.

Consider the quadrilateral AMCH.

Since AM is perpendicular to BC, and AH is perpendicular to CD, then the angle AMC = AHC = 90.

The sum of the angles of the quadrilateral is 360, then the angle МАH = 360 – 10 – 90 – 90 = 170.

AM and AH are the heights of the rhombus, and since the heights of the rhombus are equal, AM = AH, and the triangle AHM is isosceles.

Angle АМH = АНМ = (180 – МАH) / 2 = (180 – 170) / 2 = 5.

Answer: The angles of the triangle AMH are 5, 170, 5.



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