The following steps are used to construct the angle 135

1. Draw a line AB and take O on it.

2. Draw an arc with O as center and any radius, so that it cuts AB in points C and F.

3. Now take C as center and with the same radius in step 2, mark an arc which intersect the arc at D.

Now, with D as center and same radius, mark an arc which intersect the arc in E.

4. Take D and E as center, draw two arcs which intersect at G.

5. Join OG, which intersects the arc in I.

Now ∠GOA = ∠GOA = 90

6. Again, take I and F as centres, draw two arcs which intersect at J.

Now join OJ. Here ∠GOJ = 45

So, ∠JOB = ∠GOB + ∠GOJ

=> ∠JOB = 90 + 45

=> ∠JOB = 135

So, ∠JOB is the angle measuring 135