how to construct 135 degree using ruler and compasses

The below given steps will be followed to construct an angle of 135°.

(1) Draw a line *l* and mark a point P on it. Now taking P as centre and with a convenient radius, draw a semi-circle which intersects line *l* at Q and R.

(2) Taking R as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at S.

(3) Taking S as centre and with the same radius as before, draw an arc intersecting the arc at T (see figure).

(4) Taking S and T as centre, draw arcs of same radius to intersect each other at U.

(5) Join PU. Let it intersect the arc at V. Now taking Q and V as centres and with radius more than QV, draw arcs to intersect each other at W.

(6) Join PW which is the required ray making 135° with line *l*.