Answer :

(i) To construct 30°.

Given to construct an angle of 30°

*Steps for construction*:

a. Draw a ray AB of any length.

b. Now as point A is the initial point as the centre, draw an arc any radius such that, the arc meets the ray AB at point C.

c. With C as centre and with the same radius as before, draw another arc cutting the previous one at point D.

d. With D and C are centers and with same radius (which is more than half of the length of CD), draw two arcs intersecting at E.

e. Draw the ray AE, which forms an angle of 30° at point A.

Hence the ∠ EAB = 30°.

(ii) To construct

Given to construct an angle of

*Steps for construction*:

a. Draw a ray AB of any length.

b. Now as point A is the initial point as the centre, draw an arc any radius such that, the arc meets the ray AB at point C.

c. With C as centre and with the same radius as before, draw another arc cutting the previous one at point D.

d. Now with D as centre and with the same radius, draw an arc cutting the first arc (drawn in step ii) at point E.

e. With E and D as centers, and with a radius more than half the length of DE, draw two arcs intersecting at point F.

f. Join points A and F. The angle formed by FAB is 90°. i.e.

∠ FAB = 90°.

g. Now, consider G as the point where the first arc (from step ii) meets the line AF and point C where the first arc (from step ii) meets the line AB.

With G and C as centers and with any radius more than half the length of GC, draw two arcs which intersect at point H.

h. Join points A and H, thus the line forms an angle 45° with the ray AB.

i. The point where the first arc (from step b) intersects the ray AH is the point I. With I and C as centers, with any radius more than half of the length of IC, draw two arcs meeting at point J.

j. Now join points J and A, then the angle formed by the ray AJ with the ray AB is

Hence

(iii) To construct 15°.

Given to construct an angle of 15°

*Steps for construction*:

a. Draw a ray AB of any length.

b. Now as point A is the initial point as the centre, draw an arc any radius such that, the arc meets the ray AB at point C.

c. With C as centre and with the same radius as before, draw another arc cutting the previous one at point D.

d. With D and C are centers and with same radius (which is more than half of the length of CD), draw two arcs intersecting at E.

e. Draw the ray AE, which forms an angle of 30° at point A.

f. The ray AE intersects the first arc (from step b) at point F. With F and C as centers draw two arcs with any radius more than half of the length of FC, which intersect at G.

g. Now join points A and G. The angle formed between ray AB and AG is 15°.

Hence the ∠ GAB = 15°.

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