Question

Question 4 (ii)
Construct the following angles and verify by measuring them by a protractor:
(ii) ${105}^{\circ }$

Answer 1

(ii) ${105}^{\circ }$
Steps to construct an angle of ${105}^{\circ }$ :
1.Draw a ray PQ and draw an arc of some radius taking P as its centre, which intersects PQ at R.
2. Taking R as the centre and with the same radius as before, draw an arc intersecting the previously drawn arc at S.
3. Taking S as the centre and with the same radius as before, draw an arc intersecting the arc at T ( see figure).
4. Taking S and T as the centre, draw an arc of the same radius to intersect each other at U.
5. Join PU, let it intersect the arc at V. Taking T and V as the centre, draw arcs with radius more than $\frac{1}{2}TV$. Let these arcs intersect each other at W.
6. Join PW which is the required ray that makes an angle of ${105}^{\circ }$ with the ray PQ.

The angle so formed can be measured with the help of a protractor. It comes to be ${105}^{\circ }$