In the triangle ABC, the angle C-line BD-bisector = 28cm CD = 14cm Find: Outer angle A.

The BCD triangle formed by the BD bisector is rectangular, in which, through the CD leg and the BD hypotenuse, we define the opposite angle CBD.

SinСВD = СD / ВD = 14/28 = 1/2.

Then the angle CBD = arcsin (1/2) = 30.

Since BD is the bisector of the angle ABC, then the angle ABC = 2 * 30 = 60.

The external angle at the vertex A is equal to the sum of the two internal angles of the triangle ABC not adjacent to the angle AC. Angle DAС = ABC + AСB = 60 + 90 = 150.

Answer: The outer angle of the DAС is 150.