Question

Question 5 (f)

Construct with ruler and compasses, angles of following measures:
${135}^{\circ }$

Answer 1

Steps of construction:

(i) Draw a line PQ and take a point O on it.
(ii) Taking O as centre and convenient radius, mark an arc, which intersects PQ at A and B.
(iii) Taking A and B as centres and radius more than half of AB, draw two arcs intersecting each other at R.
(iv) Join OR. Thus, $\angle QOR=\angle POQ={90}^{\circ }$ .
(v) Draw $\overline{OD}$ the bisector of $\angle POR.$ Thus, $\angle QOD$ is the required angle of ${135}^{\circ }$.