For constructing an angle of 105∘, you need to construct a 60∘ angle too.
A 105∘ angle can be constructed by drawing a bisector between angles 120∘ and 90∘ as shown in the figure below. But it can be seen clearly that for constructing angles of 120∘ and 90 ∘, one needs to construct 60∘ first. In the image given, ∠DAB will be 60∘ .