Draw ÐPOQ of measure 75° and find its line of symmetry.
The below given steps will be followed to construct an angle of 75° and its line of symmetry.
(1) Draw a line l and mark two points O and Q on it, as shown in the figure. Draw an arc of convenient radius, while taking point O as centre. Let it intersect line l at 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 an arc of same radius to intersect each other at U.
(5) Join OU. Let it intersect the arc at V. Now, taking S and V as centres, draw arcs with radius more than SV. Let those intersect each other at P. Join OP, which is the ray making 75° with the line l.
(6) Let this ray be intersecting our major arc at point W. Now, taking R and W as centres, draw arcs with radius more than RW in the interior of angle of 75º. Let these be intersecting each other at X. Join OX.
OX is the line of symmetry for ÐPOQ = 75°.