hi alex,

that is not the right answer.

first you draw the side that is given (say BC)
then you draw one given angle on one endpt.say angle PBC,
such that P is random point on the ray.
draw the remaining angle on that point, say angle BPQ,
such that Q lies on line BC.
Draw line CA parallel to PQ such that A lies on ray BP.
Then pts. A, B, C form the required triangle.