Question

Using ruler and compasses only, draw an angle of measure ${135}^{\circ }$.

Answer 1

Steps of construction :

(i) Draw a line DC and take a point B on it.

(ii) With centre B and a suitable radius draw an arc meeting BC at P.

(iii) With centre P, cut off arcs PQ, QR and RS.

(iv) Bisect QR at T and join BT and produce it to E.

(v) Now bisect the arc KS at RL.

(vi) Join BL and produce it to A.

Now $\angle ABC={135}^{\circ }$.