Question

if the angle of a quadrilateral,taken in order are in the ratio 1:2:3:4 prove that it is a trapezium​

Answer 1

Answer:

sum of the angles in a quadrilateral = 360 degrees

given ratio = 1:2:3:4

sum of the terms of the ratio = 1+2+3+4 = 10

1st angle = 1/10 ×360 = 36

2nd angle = 2/10×360 = 72

3rd angle = 3/10 ×360 = 108

4th angle = 4/10 ×360 = 144

so it is a trapezium

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Answer 2

Given,

In trapezium ABCD in which

∠A : ∠B : ∠C : ∠D = 1 : 2 : 3 : 4

We know,

The sum of angles of the quad. ABCD = 360o

∠A = (360o x 1)/10 = 36o

∠B = (360o x 2)/10 = 72o

∠C = (360o x 3)/10 = 108o

∠D = (360o x 4)/10 = 144o

Now,

∠A + ∠D = 36o + 114o = 180o

Since, the sum of angles ∠A and ∠D is 180o and these are co-interior angles

Thus, AB || DC

Therefore, ABCD is a trapezium.