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Question

Draw $$\angle POQ$$ of measures $$75^\circ$$ and find its line of symmetry.

Solution
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The below given steps will be followed to construct an angle of $$75^\circ$$ 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 $$\dfrac{1}{2}SV.$$ Let those intersect each other at P. Join OP, which is the ray making $$75^\circ$$ 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 $$\dfrac{1}{2}RW$$ in the interior of angle of $$75^\circ.$$ Let these be intersecting each other at X. Join OX.
OX is the line of symmetry for $$\angle POQ = 75^\circ.$$

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