Question

Draw ∠POQ of measure 75° and find its line of symmetry. 

Answer 1

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 `1/2` 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 `1/2`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 ∠POQ = 75°.