Respuesta :
The statement true about opposite angles of a cyclic quadrilateral is they add up to 180 degrees .
What is cyclic quadrilateral?
A cyclic quadrilateral means a quadrilateral that is inscribed in a circle. That means there is a circle that passes through all four vertices of the quadrilateral. The vertices are said to be concyclic.
What are the properties of cyclic quadrilateral ?
Properties of a cyclic quadrilateral are given below:
In a cyclic quadrilateral, all the four vertices of the quadrilateral lie on the circumference of the circle.
- The four sides of the inscribed quadrilateral are the four chords of the circle.
- The measure of an exterior angle at a vertex is equal to the opposite interior angle.
- In a cyclic quadrilateral, p × q = sum of product of opposite sides, where p and q are the diagonals.
- The perpendicular bisectors are always concurrent.
- The perpendicular bisectors of the four sides of the cyclic quadrilateral meet at the center
- The sum of a pair of opposite angles is 180° (supplementary).
According to the question
The statement true about opposite angles of a cyclic quadrilateral
As per properties of cyclic quadrilateral :
- The sum of a pair of opposite angles is 180° (supplementary).
i.e
they add up to 180 degrees
Hence, The statement true about opposite angles of a cyclic quadrilateral is they add up to 180 degrees .
To know more about cyclic quadrilateral and their properties here:
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