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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

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