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We can draw  105 degree angle by using a compass by the following way:1. Draw a line AB
2. Placing the compass in A, take some randon length in the compass and draw an arc cutting AB at the point C.
3. Now without changing the length in the compass draw another arc cutting the previous arc at the point D by placing the compass in C.
4. Join AD.
5. Set half the length of AD as the compass length.
6. Keeping the compass at A and D draw arcs on both sides of the line AD.
7. The arcs of both sides of AD form two points, join those points which cuts the line AD at E. This line is the perpendicular bisector of line AD.
8. Take the length on the compass as AE and keeping the compass at E
draw an arc cutting the perpendicular bisector at F.
9. Join AF. < BAF = 105 

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First draw an angle of 90 and then draw an angle of 120 by pencil and compass
then draw their bisector with compass
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