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In a quadrilateral ABCD , the angles A ,...

In a quadrilateral `ABCD` , the angles `A , B , C and D` are in the ratio `1:2:3: 4.` Find the measure of each angles of the quadrilateral.

Text Solution

Verified by Experts

"let the angles A,B,Cand D `=x,2x,3x,4x`
from angle sum
sum of all angles`=360^@`
`x+2x+3x+4x=360^@`
`x=36^@`
so angles are`36^@,72^@,108^@,144^@`
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Knowledge Check

  • The sum of the four angles of a quadrilateral is 360^(@) . In a quadrilateral ABCD, the angles A, B, C and D are in the ratio 1:2: 4:5, then the measure of each angle of a quadrilateral is

    A
    `36^(@),60^(@),108^(@),156^(@)`
    B
    `30^(@),60^(@),120^(@),150^(@)`
    C
    `42^(@),54^(@),110^(@),154^(@)`
    D
    `72^(@),108^(@),36^(@),144^(@)`

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