Question

How to construct a 105 degree angle with a compass and ruler

Answer 1

first draw 120 by making arc of 60 degree on both sides
aod 60. doc. 60
doc bisector doe 30 and eoc 30
eoc is bisector eof 15

Answer 2

Construction of angle 105 degree using compasses and ruler

Steps:

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

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

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).

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

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

We get the angle XOB=90 degree.

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

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

Now let’s bisect the angle YOX.

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.

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.