(i) 30°
Given: A ray OA.
Required: To construct an angle of 30° at O.
Steps of Construction:
1. Taking O as centre and some radius, draw an arc of a circle, which intersects OA, say at a point B.
2. Taking B as centre and with the same radius as before, draw an arc intersecting the previously drawn arc, say at a point C.
3. Draw the ray OE passing through C. Then ∠EOA = 60°.
4. Taking B and C as centres and with the radius more than BC, draw arcs to intersect each other, say at D.
5. Draw the ray OD. This ray OD is the bisector of the angle EOA, i.e.,