# Draw AngleDEF = 72degree. Construct 3/4 AngleDEF using compass.Please answer my question urgently. My exam is on 20th Thursday.

As you cannot construct an angle of 72$°$ using compass and ruler. You can easily draw angles which are multiples of 15$°$ with the help of compass.
So first you draw an angle of 72$°$ with the help of a protractor and then you can construct  $\frac{3}{4}$ of that angle.
Steps of construction for  54$°$ angle.
1) Draw a ray XY .
2) Draw $\angle$AXY = 72$°$ 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 = $\frac{3}{4}×72°=54°$

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

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