Question

Question 5 (e)

Construct with ruler and compasses, angles of following measures:
${45}^{\circ }$

Answer 1

Steps of construction:

(i) Draw a ray $\overline{OA}$
(ii) Taking O as centre and convenient radius, mark an arc, which intersects $\overline{OA}$ at X.
(iii) Taking X as centre and the same radius, cut the previous arc at Y.
(iv) Taking Y as centre and the same radius, draw another arc intersecting the same arc at Z.
(v) Taking Y and Z as centres and the same radius, draw two arcs intersecting each other at S.
(vi) Join OS and produce it to form a ray OB. Thus, $\angle$ BOA is of ${90}^{\circ }$.
(vii) Draw the bisector of $\angle BOA.$ Thus, $\angle MOA$ is the required angle of ${45}^{\circ }$.