Question

Construct an angle of ${105}^{\circ }$ using a compass and verify by measuring it by a protractor.

Answer 1

Construction :

Steps:
1. Take the given ray PQ. Draw an arc of some radius taking P as its centre, which intersects PQ 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 PU. Let it intersect the arc at V. Taking T and V as centre, draw arcs with radius more than $\frac{1}{2}TV$.
6. Let these arcs intersect each other at W. Join PW which is the required ray making ${105}^{\circ }$ with the given ray PQ.

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