How do you construct an angle of 105 degrees using compass?

Answer 1

Using only a compass you cannot do it - you will need a straight edge as well.

Draw a straight line AB.

From A, using the length AB draw an arc above AB.

From B, using the length AB draw an arc to intersect the first arc at C.

Join CA.

Then angle CAB is 60%

From A, draw an arc to cut the two arm of the angle, AB and AC at X and Y respectively.

From X, draw an arc between the two arms of angle CAB.

Using the same length, repeat from Y so as to cut the previous arc at D.

Join DA.

DA bisects angle CAB and so angle DAB = 30 degrees.

Now bisect angle DAB to give angle EAB = 15 degrees.

At A, draw a perpendicular (facing downwards). If F is any point on the perpendicular, the angle EAF = 15 + 90 = 105 degrees.