Construct the angles of the following measurements:
(i) 30°
(ii) 75°
(iii) 105°
(iv) 135°
(v) 15°
(vi) 22(1/2)°
(i) Steps of construction:
1. Draw a line segment AB.
2. Keeping A as the centre and any radius draw an arc which intersects AB at C.
3. Keeping C as center and the same radius draw an arc which intersects the previous arc at D.
(ii) Steps of construction:
1. Draw a line segment AB
2. Keeping A as center and any radius draw an arc which intersects AB at C
3. Keeping C as center and the same radius draw an arc which intersects the previous arc at D
4. Keeping D as center and same radius draw an arc which intersects arc in (2) at E
5. Keeping E and D as center and radius more than half of ED, draw arcs intersecting each other at F
6. Join FA which intersects arc in (2) at G
7. Keeping G and D as center and radius more than half of GD draw arcs intersecting each other at H
8. Join HA
Therefore ∠HAB = 75°
4. Keeping D and C as center and radius more than half of DC draw arcs which intersect each other at E.
5. Join EA.
Therefore ∠EAB = 30°
(iii) Steps of construction:
1. Draw a line segment AB.
2. Keeping A as the center and any radius draw an arc which intersects AB at C.
3. Keeping C as center and the same radius draw an arc which intersects the previous arc at D.
4. Keeping D as the centre and same radius draw an arc which intersects arc in (2) at E.
5. Keeping E and D as center and radius more than half of ED draw arcs which intersect each other at F.
6. Join FA which intersects arc in (2) at G.
7. Keeping E and G as center and radius more than half of EG draw arcs which intersect each other at H.
8. Join HA.
Therefore ∠HAB = 105°
(iv) Steps of construction:
1. Draw a line segment AB and produce BA to C.
2. Keeping A as the center and any radius draw an arc which intersects AC at D and AB at E.
3. Keeping D and E as center and radius more than half of DE draw arcs which intersect each other at F.
4. Join FA which intersects the arc in (2) at G.
5. Keeping G and D as center and radius more than half of GD draw arcs which intersect each other at H
6. Join HA.
Therefore ∠HAB = 135°
(v) Steps of construction:
1. Draw a line segment AB.
2. Keeping A as the centre and any radius draw an arc which intersects AB at C.
3. Keeping C as center and the same radius draw an arc which intersects the previous arc at D.
4. Keeping D and C as center and radius more than half of DC draw arcs which intersect each other at E.
5. Join EA which intersects arc in (2) at F.
6. Keeping F and C as center and radius more than half of FC draw arcs which intersect each other at G.
7. Join GA.
Therefore ∠GAB = 15°
(vi) Steps of construction:
1. Draw a line segment AB.
2. Keeping A as the center and any radius draw an arc which intersects AB at C.
3. Keeping C as center and the same radius draw an arc which intersects the previous arc at D.
4. Keeping D as the centre and same radius draw an arc which intersects arc in (2) at E.
5. Keeping E and D as center and radius more than half of ED draw arcs which intersect each at F.
6. Join FA which intersects arc in (2) at G.
7. Keeping G and C as center and radius more than half of GC draw arcs intersecting each other at point H.
8. Join HA which intersects the arc in (2) at a point I.
9. Keeping I and C as center and radius more than half of IC draw arcs intersecting each other at point J.
10. Join JA.
Therefore ∠JAB = 22(1/2)°
