Question

Construct with ruler and compass, angle of 135° measure.

Answer 1

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 `1/2`QV, draw arcs to intersect each other at W.
6. Join PW which is the required ray making 135° with line l.