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The opposite angles of a parallelogram a...

The opposite angles of a parallelogram are equal.

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Let `ABCD` be the given parallelogram.
So, `AD` parallel `BC` and `AB` parallel `DC`.
Let `/_A=x`
Then `/_D=180^@-/_A= 180^@- x` (Because `/_A` and `/_D` are interior opposite angles)
`/_C=180^@-/_D=x`
`∠B=180^@-/_A=180^@-x`
Thus, we can see that the opposite angles `angleA` and `angleC` are equal; and the opposite angles `angleB` and `angleD` are also equal.
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Knowledge Check

  • Assertion : Two opposite angles of a parallelogram are (3x-2)^(@) and (50 - x)^(@) . The measure of one of the angle is 37^(@) . Reason : Opposite angles of a parallelogram are equal

    A
    If both assertion and reason are true and reason is the correct explanation of assertion
    B
    If both assertion and reason are true but reason is not the correct explanation of assertion.
    C
    If assertion is true but reason is false.
    D
    If assertion is false but reason is true.

  • The opposite angles of a parallelogram are (3x-2)^(@)and(150-x)^(@). Find each angle of the parallelogram.

    A
    `110^(@),70^(@),110^(@),70^(@)`
    B
    `111^(@),69^(@),111^(@),69^(@)`
    C
    `112^(@),68^(@),112^(@),68^(@)`
    D
    `109^(@),71^(@),109^(@),71^(@)`

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