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In a quadrilateral A B C D , the angles ...

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

Text Solution

Verified by Experts

Let the angle A `=1x`
angle B`=2x`
angle C`=3x`
angle D `=4x`
we know that the sum of the angles of a quadrilateral is `360^0`
angle `A+B+C+D=360^@`
`x+2x+3x+4x=360^@`
`10x=360^@`
`x=36^@`
Angle A `=x=36^@`
Angle B`=2xxx=72^@`
Angle C`=3xxx=108^@`
Angle D`=4xxx=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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