How do you construct angle 135 degrees?

Answer 1

Note that 135 = 90 + 45.

So first construct a right angle, and then bisect the "back" half of it:

1. Draw (horizontal) straight line XAB
2. Construct the perpendicular bisector at A:
   1. With the point of your compasses on A draw arcs either side of it on line segments AX and AB.
   2. Open your compasses wider, with the point on where the arc in step 2.1 cuts (intersects) AB, draw an arc above the line XAB.
   3. With the compasses set the same, with the point on where the arc in step 2.1 cuts AX, draw an arc to cut the arc drawn in step 2.
   4. Mark the point where the arcs cut as Y.
   5. Draw in line AY.
3. Bisect angle XAY:
   1. With the point of the compasses on A, draw arcs on lines AX and AY
   2. With the point of the compasses on where the arc drawn in step 3.1 cuts AX, draw an arc between AX and AY.
   3. With the compasses set the same, with the point on where the arc in step 3.1 cuts AY, draw an arc to cut the arc drawn in step 2.
   4. Mark the point where the arcs cut C.
   5. Draw in line AC
4. Angle CAB is 135o

In drawing the arcs to cut, if they don't cut you may have to either increase the distance between the point and "pencil" of your compasses and/or redraw the arcs longer.