if the angle of a quadrilateral,taken in order are in the ratio 1:2:3:4 prove that it is a trapezium
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Answered by
15
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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Answered by
76
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.
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