The height DM is drawn in the triangle BDA. Find the angles of a triangle DMA if its outside angle

The height DM is drawn in the triangle BDA. Find the angles of a triangle DMA if its outside angle at apex A is 135 degrees, BD = DA.

The external angle DАЕ is adjacent to the internal angle DАВ, then the angle DAV = (180 – DAE) = (180 – 135) = 45.

Since, according to the condition, BD = DA, then the triangle ABD is isosceles, then the angle ABD = DAB = 45.

DМ is the height of the triangle ВDА, then the angle DМВ = 90, and the angle АDM = (180 – 90 – 45) = 45.

Answer: The angles of the triangle DMA are 45, 45, 90.