Question

Construct the following angles and verify by measuring them by a protractor:
(i) ${75}^{\circ }$

Answer 1

(i) ${75}^{\circ }$
Steps to construct an angle of ${75}^{\circ }$ :
1. Draw a ray PQ and draw an arc of some radius taking point 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.
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.
6. Taking S and V as the centre, draw arcs with radius more than $\frac{1}{2}SV$.
7. Let those intersect each other at W. Join PW which is the required ray that makes an angle of ${75}^{\circ }$ with the ray PQ.

The angle so formed can be measured with the help of a protractor. It comes to be ${75}^{\circ }$