Question

The angles A, B,CD of a quadrilateral in the rattio 2:4:5:7. Find the measures of these angles. What type of quadrilateral is it? Give reasons.

Answer 1

Let the angles of ABCD be 2x, 4x, 5x and 7x

2x + 4x + 5x + 7x = 360o

18x = 360o

x = 20o

So, the angles are A = 40o, B = 80o, C = 100oand D = 140o

A + D = 40o + 140o = 180o

B + C = 80o + 100o = 180o

So, ABCD is a trapezium with AB parallel to CD.

Answer 2

Let the angles of quadrilateral be A=2x,B=4x,C=5x & D= 7x.

Using Angle Sum property(ASP):

2x+4x+5x+7x = 360°

18x= 360°

x=360°/18

x= 20°

Therefore, angles are:

A= 2x=2(20)=>40°,

B=4x=4(20)=>80°

C=5x= 5(20)=>100° &

D=7x=7(20)=>140°

Here,

A+D=40°+140°=180°

&

B+C=80°+100°=180°

Hence, the angles are 40°,80°,100° &140° and it is a trapezium with AB||CD.

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