Steps of construction:

Step 1: Draw a ray OY.

Step 2: An arc BAE is drawn taking O as a centre.

Step3: With E as a centre, 2 arcs A and C are made on the arc BAE.

Step 4: Taking A and B as centre one by one, arcs are made to intersect at X and ∠XOY = is drawn.

Step 5: Taking A and C as centres, arcs are made to intersect at D.

Step 6: OD is joined and hence, ∠DOY = is constructed.

Thus, ∠DOY is the required angle

(ii)

Steps of construction:

Step 1: Draw a ray OY.

Step 2: Taking O as a centre an arc ABC is drawn.

Step 3: With A as a centre, two arcs B and C are made on the arc ABC.

Step 4: Now, taking B and C as centres, arcs are made to intersect at E and ∠EOY = 90⁰is made.

Step 5: With B and C as centres, arcs are made to intersect at X.

Step 6: OX is joined and hence ∠XOY = 105⁰ is constructed.

Thus, ∠XOY is the required angle

(iii)

Steps of construction:

Step 1: A ray DY is drawn.

Step 2: An arc ACD is drawn with O as a centre.

Step 3: With A as a centre, two arcs B and C are made on the arc ACD.

Step 4: With B and C as centres, arcs are made to intersect at E and ∠EOY = 90⁰is made.

Step 5: With F and D as centres, arcs are made to intersect at X or bisector of angle EOD is constructed.

Step 6: OX is joined and ∠XOY = 135⁰ is constructed.

Thus, ∠XOY is the required angle