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The sum of either pair of opposite angle...

The sum of either pair of opposite angles of a cyclic quadrilateral is `180^0` OR The opposite angles of a cyclic quadrilateral are supplementary.

Text Solution

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TO prove`=/_A+/_C=180^@,/_B+/_DD=180^@`
Chord AB`/_ACB=/_ADB-(1)`
Chord BC`/_BAC=/_BDC-(2)`
adding equation 1 and 2
`/_ACB+/_BAC=/_ADB+/_BDC`
`/_ACB+/_BAC+/_ABC=/_ADC+/_ABC`
`/_D+/_B=180^@`
`/_B+/_D=180^@`
...
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The opposite angles of a cyclic quadrilaterals are supplimentary

Theorem 10.11 : The sum of either pair of opposite angles of a cyclic quadrilateral is 180º.

Knowledge Check

  • If an exterior angle of a cyclic quadrilateral be 50^@ , then the interior opposite angle is :

    A
    `130^@`
    B
    `40^@`
    C
    `50^@`
    D
    `90^@`

  • The quadrilateral formed by angle bisectors of a cyclic quadrilateral is a :

    A
    rectangle
    B
    square
    C
    parallelogram
    D
    cyclic quadrilateral

  • The quadrillateral formed by angle bisectors of a cyclic quadrilateral is a:

    A
    rectangle
    B
    square
    C
    parallelogram
    D
    cyclic quadrilateral

    • Similar Questions

    Explore conceptually related problems

    Prove that the sum of opposite pair of angles of a cyclic quadrilateral is 180^(@)

    Definition of Cyclic quadrilateral

    ABCD is a cyclic quadrilateral (see Figure). Find the angles of the cyclic quadrilateral.

    If the sum of any pair of opposite angles of a quadrilateral is 180^(@) ; then the quadrilateral is cyclic.

    Theorem 10.12 : If the sum of a pair of opposite angles of a quadrilateral is 180º, the quadrilateral is cyclic.

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