As u cannot construct an angle of 72 using ruler and compass , u can easily draw angles with the multiple of 15 with the help of compass.
so first u draw an angle of 72 with the help of a protractor and then u can construct 3/4 of that angle.
steps for construction of 54 degree angle :
a) draw a ray XY.
b) draw ∠AXY = 72 using protractor.
c) taking X as center and any convenient radius , draw an arc intersecting AX and XY at O and P respectively.
d) taking P and O as centers and radius more than half of OP , draw 2 arcs intersecting at M.
e) draw a ray XB passing through M . let this ray intersect arc OP at Q .
f) taking Q and O as centers , and radius more than half QO , draw 2 arcs intersecting at N.
g) draw ray XC passing through N.
thus ∠CXY = 3/4 of 72 = 54