Question

Construct the following angles and bisect them.
75
105
​

Answer 1

1. 75°

Steps of Construction :- ( also refer the 1st attached file ↑)

(i) Draw a line segment BC.

(ii) At B, draw an angle ABC equal to 75°.

(iii) With centres P and T, draw arcs intersecting each other at L.

(iv) Join BL and produce it to D. Then BD bisects ∠ABC.

2. 105°

Steps of Construction :- (also refer the 2nd attached file ↑)

(I) A ray OA is drawn.

(ii) An arc is drawn with O as a centre.

(iii) With the same length AB construct another arc from B

(iv) Construct a perpendicular bisector to another arc which is D.Join OD

∴∠AOC=90°

(v) Construct a perpendicular bisector from C to another point of the arc .Join OD

∴∠AOD=105°

Thus,∠AOD is the required angle making 105°