Draw ∠POQ of measures 75∘ and find its line of symmetry.
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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 21SV. 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 21RW in the interior of angle of 75∘. Let these be intersecting each other at X. Join OX. OX is the line of symmetry for ∠POQ=75∘.