Question

Draw an angle of 60° using ruler and compasses and divide it into four equal parts. Measure each part.

Answer 1

Steps of construction:

(i) Draw a ray `vec(OA)`

(ii) With O as centre and any convenient radius draw an arc meeting the rav OA at X.

(iii) With X as centre and the same radius draw an arc which cuts the previously drawn arc at U.

(iv) Join OU and produce it to any point B. So ∠BOA = 60°.

(v) Now with centre X and U and radius more than `1/2(hat(UX))` draw the arcs on the same side of ∠BOA which cuts each other at V.

(vi) Join OV and produce it any point C as well as it cuts the arc `hat(UX)` at W.

(vii) Again with the centre X and W and radius more than `1/2(hat(WX))` draw the arcs on the same side of ∠BOA which cuts each other at Z.

(viii) Join OZ and produce it to any point D.

(ix) With the centre U and W and radius more than `1/2 (hat(UW))` draw the arcs on the same side of ∠BOA with cuts each other at the point P.

(x) Join OP and produce it to any point E. Now with the help of protractor we observe that each angle i.e, ∠BOE = ∠EOC = ∠COD = ∠DOA = 15°.