Question

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

Answer 1

Step-by-step explanation:

Let the angles be x,2x,3x,4x

Sum of all angles of a quadrilateral=360°

So x+2x+3x+4x=360°

x=36°

Therefore angles of quadrilateral are 36,72,108,144

72+108=180 AND 36+144=180

This suggests that quadrilateral is a trapezium because

Trapezium has sum 180° of any two pairs of adjacent angles

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.