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=75o
(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 =105o
(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 = 135o
(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 =15o
(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=221/2o