Question

Question 4 (iii)
Construct the following angles and verify by measuring them by a protractor:
(iii) ${135}^{\circ }$

Answer 1

(iii) ${135}^{\circ }$
Step to construct an angle of ${135}^{\circ }$ :
1. Draw a ray PQ, and extend PQ to the left side of P. Draw a semi-circle of some radius taking point P as its centre, which intersects PQ at R and W.
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 same radius to intersect each other at U.
5. Join PU, let it intersect the arc at V. Taking V and W centre and with radius more than $\frac{1}{2}VW$, draw arcs to intersect each other at X.
6. Join PX, which is the required ray that makes an angle of ${135}^{\circ }$ with the ray PQ.

The angle so formed can be measured with the help of protractor . It comes to be ${135}^{\circ }$