how to draw 105 and 135 degrees with compass?

1. Construction of angle 105 degree using compass:(Refer attached image)

Steps:

1. Draw a line AB and mark point O on it where angle is to be drawn.


2. With O as center draw an arc (semicircle) which intersects the line AB at points H and I.


3. Keeping the same radius as above and H as center, draw an arc which intersects the semicircle at point C. Without changing the radius as above and C as center, draw an arc which intersects the semicircle at point D. (The points C and D correspond to 60 and 120 degrees angle respectively).


4. Now draw two arcs of same radius keeping the centers as C and D respectively which intersect at point E.


5. Join points E and O and extend it to point X.


6. We get the angle XOB=90 degree.


7. Join the points O and D and extend it to point Y, so we get angle YOB=120 degree.


8. Angle YOX=Angle YOB-Angle XOB=120-90=30 degree


9. Now let’s bisect the angle YOX.


10. Draw two arcs of same radius keeping the centers D and F (point of intersection of EO and semicircle) which intersect at point G. Join GO.


11. We get the angle GOB=105 degree.

Note: We have constructed angle of 105 degree as sum of two angles of 90 and 15 degrees. Alternately it can be constructed as sum of two angles of 60 and 45 degrees.

2. Construction of angle 135 degree using compass: (Refer attached image)

1. Repeat steps 1 to 6 as stated above.


2. Now let’s bisect angle YOA=90 degree. Draw two arcs of same radius keeping the centers F and G respectively, which intersect at point H.


3. Join points H and O and extend it to point Y.


4. We get the angle YOB =135 degree.