Draw AngleDEF = 72degree. Construct 3/4 AngleDEF using compass.

Please answer my question urgently. My exam is on 20th Thursday.

So first you draw an angle of 72$\xb0$ with the help of a protractor and then you can construct $\frac{3}{4}$ of that angle.

Steps of construction for 54$\xb0$ angle.

1) Draw a ray XY .

2) Draw $\angle $AXY = 72$\xb0$ using protractor.

3)Taking X as centre and any convenient radius,draw an arc intersecting AX and XY at O and P respectively.

4) Taking P and O as centres and radius more than half OP, draw two arcs intersecting at M.

5) Draw a ray XB passing through M. Let this ray intersect the arc OP at Q.

6)Taking Q and O as centres and radius more than half QO, draw two arcs intersecting at N.

7)Draw a ray XC passing through N.

Thus $\angle $CXY = $\frac{3}{4}\times 72\xb0=54\xb0$

Justification:-

Here we first draw $\angle $AXY= 72$\xb0$.Then bisect this angle to get $\angle $BXY= 36$\xb0$.Then again bisect the angle between AX and BX to get $\angle $CXY= 54$\xb0$

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