Construct the following angles and verify by measuring them by a protractor: (i) 75° (ii) 105° (iii) 135°

I/Steps of construction
(i) Draw a ray AB at the point A.
(ii) Taking A as centre and a convenient radius, draw an arc which intersect AB at C.
(iii) Taking C as centre and with the same radius, draw an arc which intersect the previous arc at F.
(iv) Similarly, taking E as centre and with the same radius, draw an arc which intersect at E.
(v)Taking E and F as as center, draw arcs with equal radius (more than half of EF). which intersect at H.
(vi) Draw a ray AH which intersects the main arc at D.
(vii) Taking F and D as centre, draw arcs with equal radius (more than half of FD), which intersect at G.
(viii) Draw a ray AG. ∠GAB is the required angle of 75°.

II/Steps of construction.
(i) Draw a ray AB at the point A.
(II) Taking A as centre and a convenient radius, draw an arc which intersect AB at C.
(iii) Taking C as center and with the same radius, Draw an arc which intersect the previous arc at D.
(iv) Similarly, taking E as centre and with the equal radius, draw an arc which intersect at G.
(v) Taking D and G as centre, draw arcs with same radius (more than half of DG), which intersect at F.
(vi) Draw a ray AF which intersects the main arc at E.
(vii) Taking E and G as centre, draw arcs with equal radius (more than half of EG), which intersect at H.
(viii) Draw a ray AH. ∠HAB is the required angle of 105°.

III/Steps of construction.
(i) Draw a ray AD at the point A.
(II) Taking B as centre and a convenient radius, draw an arc which intersect AD at C.
(III) Taking C as centre and with the same radius, draw an arc which intersect the previous arc at P.
(iv) Similarly, Taking P as centre and with the equal radius, draw an arc which intersect at F.
(v) Taking P and F as centre, draw arcs with same radius (more than half of PF), which intersect at H.
(vi) Draw a ray BH from the point B.
(vii) Taking B as center, draw an arc taking some radius, which intersects AB at E and BH at Q.
(viii) Taking E and Q as centre, draw arcs with equal radius (more than half of EQ), which intersect at G.
(ix) Draw a ray BG. ∠GBD is the required angle of 135°.