SOL:(i)

**Steps of construction:**

1. Draw a line segment AB.

2. With center A and any radius, draw an arc which intersect AB at C.

3. With center C and same radius, draw an arc which intersects previous arc at D.

4. With centers D and C and radius more than DC/2 draw arcs intersecting each other at E

5. Join EA

∠EAB = 30o

**(ii)**

^{}

**Steps of construction:**

1. Draw a line segment AB.

2. With center A any radius, draw an arc which intersect AB at C.

3. With center C and same radius, draw an arc which intersects previous arc at D.

4. With center D and same radius, draw an arc which interest are in (2) at E

5. With centers E and D and radius more than ED/2 draw arcs intersecting each other at F.

6. Join FA which intersects arc in (2) at G

7. With centers G and D, and radius more than GD/2 draw arcs intersecting each other at H.

8. Join HA

Therefore,∠HAB=75^{o}

(iii)

^{}

**Steps of construction:**

1. Draw a line segment AB.

2. With center A and any radius, draw an arc which intersect AB at C.

3. With center C and same radius, draw an arc which intersects previous arc at D.

4. With center D and same radius, draw an arc which interest are in (2) at E

5. With centers E and D and radius more than ED/2 draw arcs intersecting each other at F.

6. Join FA which intersects arc in (2) at E

7. With centers E and G, and radius more than half of EG, draw arcs intersecting each other at H.

8. Join HA

∠HAB =105^{o}

**(iv)**

^{}

**Steps of construction:**

1. Draw a line segment AB and produce BA to pint C

2. With center A and any radius, draw an arc which intersect AC to D and AB at E.

3. With center D and E and radius more than half of DE, draw two arcs which intersects each other at F.

4. Join FA which intersect the arc in (2) at G

5. With center G and D radius more than GD/2 draw two arcs which intersect each other at H

6. Join HA

∠ HAB = 135^{o}

**(v)**

^{}

**Steps of construction:**

Step 1: Draw a line segment AB

Step 2: with center A and any radius, draw an arc which intersects previous arc at C

Step 3: with center C and same radius, draw an arc which intersect previous arc at D

Step 4: with center D and C radius more than half of DC draw arcs intersecting each other at E

Step 5: Join EA which intersects arc in (2) at F.

Step 6: With centers F and C and radius more than FC/2 draw arcs intersecting each other

Step 7: Join GA

Therefore ∠GAB =15^{o}

(vi)

^{}

**Steps of construction:**

Step 1: Draw a line segment AB

Step 2: with center A and any radius, draw an arc which intersects AB at C

Step 3: with center C and same radius, draw an arc which intersect previous arc at D

Step 4: with center D and same radius, draw an arc which intersects arc in (2) at E.

Step 5: with center E and D and radius more than half of ED, draw arcs intersecting each other at F.

Step 6: Join FA which intersects arc in (2) at G

Step 7: with center G and C and radius more than half of GC, draw arcs intersecting each other at H

Step 8: Join HA which intersects arc in (2) at 1.

Step 9: with centers I and C and radius more than half of IC, draw arcs intersecting each other

Step 10: Join JA

∠JAB=221/2^{o}