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Diagonals of a quadrilateral A B C D b...

Diagonals of a quadrilateral `A B C D` bisect each other. If `/_A=45^@,` then `/_B=` `115^@` (b) `120^@` (c) `125^@` (d) `135^@`

Text Solution

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Given: ABCD is a quadrilateral.
`angle A=45^@`
Solution: `angleA+angleB=180^@`
( diagonals of a quadrilateral bisects each other hence ABCD is a parallelogram )
`45^@+angleB=180^@`
`angleB=135^@`

Hence, option (d) is correct.
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Knowledge Check

  • Diagonals of a quadrilateral bisect each other. If angle A = 45^(@) , then angle B equals

    A
    `45^(@)`
    B
    `55^(@)`
    C
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    C
    rectangle
    D
    kite

  • If the diagonals of a quadrilateral bisect each other at right angles, then this quadrilateral is

    A
    a rectangle
    B
    a rhombus
    C
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    D
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