Draw a straight line and mark a point as the vertex.
Use a compass to draw an arc centered at the vertex, cutting the line at one point.
Without changing the compass width, place the compass on that cut point and draw another arc to intersect the first arc.
Draw a line from the vertex through the arc intersection to form a 60 degree angle.
Extend the original line in the opposite direction through the vertex.
Use the compass to bisect the 60 degree angle by drawing equal arcs from its two arms and joining the vertex to the arc intersection, forming 30 degrees.
Copy the 30 degree angle adjacent to the 60 degree angle on the straight line to make 90 degrees.
Copy the 45 degree angle adjacent to the 90 degree angle by bisecting the 90 degree angle.
The angle formed between the original line direction and the new ray is 135 degrees.