Question

Construct the following angles and verify by measuring them by a protractor:
${105}^{\circ }$

[3 marks]
[NCERT]
[Construction of an Angle Bisector]

Answer 1

Solution:

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.
[1 mark]

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.
[1 mark]

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 ${105}^{\circ }$
[1 mark]