Question

Construct with ruler and compass, angle of 45° measure.

Answer 1

The below given steps will be followed to construct an angle of 45°.

1. Draw a line l and mark a point P on it. Now taking P as centre and with a convenient radius, draw an arc of a circle which intersects line l at Q.
2. Taking Q as centre and with the same radius as before, draw an arc intersecting the previously drawn arc at R.
3. Taking R as centre and with the same radius as before, draw an arc intersecting the arc at S (see figure).
4. Taking R and S as centres, draw arcs of same radius to intersect each other at T.
5. Join PT. Let it intersect the major arc at point U.
6. Taking Q and U as centres, draw arcs with radius more than QU to intersect each other at V. Join PV.
   PV is the required ray making 45° with the given line l.