How do you construct 22.5 degree with compass?

asuming you know how to construct a 60 degree angle, you would start by drawling a basic construction line an then make your angle bisecter with breaks the angle into 30 degree angles. then create another angle bisector for 30 degrees breaking it into 15 degree angles. then do the same with the 15 degree angle. your drawling sould have three angle bisectors for each angle.

to get your answer of 22.5 degress angle, simply add the 15 degree angle you drew with the 7.5 angle you got from spliting the 15 degree angle in half

its hard to explain without drawing it out..... hope this helps