Construction of a triangle, given: side, sum of the other sides and angle between them. Given: $\overline{AB}$, $\overline{AC}+\overline{BC}$ and $\angle C$. Construct the triangle $\triangle ABC$ using rule and compass.

Draw the side given AB
draw the angle given A
produce the adjacent side which equal to sum of given sides AP
connect remaining point from it  PB
bisect that side PB
produce that side until cut AP
take the point of intersection C now you have triangle.  
