Question

Construction of angles of all the multiple of 15 till 180

Answer 1

Start with 60°: 
draw a circle centered at point P. 
draw another circle centered at any point, Q, on the circle, with same radius. 
Call the points where the two circles intersect R and S. 
Angle PQR = QPR = PQS = QPS = 60° 

Bisect that angle to get 30°. 
Bisect the 30° to get 15. 

(Bisection is a basic construction which I won't elaborate.) 

Then you can just keep constructing adjacent 15's for each multiple. 

Here are some special cases: 

Then if the 15 shares an edge with 60, you get 45 (the rest of the 60). 

Now have 15, 30, 45, and 60. 

For 75, repeat the above so that the new 15 is adjacent to the original 60 (may need more circles). 

For 90, bisect 180. 

120 = 180 - 60. 

For 105 and 135, just construct 15 adjacent to 120 on both the inside and outside. 

150 = 180 - 30 and 
finally 165 = 150 + 15.