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The angles of a quadrilateral are 110^@,...

The angles of a quadrilateral are `110^@, 72^@, 55^@ and x^@` Find the value of `x^@`

Text Solution

Verified by Experts

Given:
Angles of quadrilateral are:`110^@,\ 72^@,\ 55^@` and `x^@`
By angle sum property of quadrilateral, we state that the sum of all four angles of the quadrilateral is equal to `360^@`.
`therefore110^@\+72^@\+55^@\+x^@=360^@`
`x^@+237^@=360^@`
`x^@=360^@-237^@`
`x^@=123^@`
Hence, the value of the fourth angle is `123^@`.
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Knowledge Check

  • Three angles of a quadrilateral measure 110^(@), 82^(@) and 68^(@) . Find the measure of the fourth angle.

    A
    `80^(@).`
    B
    `100^(@).`
    C
    `200^(@).`
    D
    `70^(@).`

  • The angles of quadrilateral are x-20^(@), 2x^(@), x+20^(@) , and x+30^(@) . Find the smallest angle of the quadrilateral.

    A
    `66^@`
    B
    `56^@`
    C
    `36^@`
    D
    `46^@`

  • The angles of quadrilateral are x-5^(@),x,x+5^(@),and x+10^(@) . Find the smallest angle of the quadrilateral.

    A
    `90^(@)`
    B
    `(82 1/2)^@`
    C
    `(82 3/4)^@`
    D
    `(79 1/4)^@`

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