How do you draw 105 degree angle?

Answer 1

Easiest is to use a protractor.

Alternative: Draw a 90 degree angle.

Bisect the external angle so that it is 45 degrees.

Trisect that angle so that the angle adjacent to the 90 degree angle is 15 deg

Then 90 + 15 degrees = 105 degrees.

Both, bisection and trisection require the use of a compass (and ruler).