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Question

If the angles of a quadrilateral takes in order are proportional to 1:2:3:4 . Prove that it is trapezium.

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Solution

Angles of a quadrilateral are in ratio 1:2:3:4
Let the quadrilateral be ABCD
A:B:C:D=1:2:3:4
Let A=x
x:2x:3x:4x=A:B:C:D
We know that
A+B+C+D=360o
x+2x+3x+4x=360o
10x=360o
x=36o
A=36o …………(1)
B=72o …………..(2)
C=108o ………….(3)
D=144o …………(4)
By adding (1) & (4)
We get
A+D=180o
By adding (2) & (3)
We get
C+B=180o
So we can conclude that AB||CD.
So it is a trapezium.

1214423_1317208_ans_0a9efad03149439ba57593c52fdd954c.jpeg

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