The opposite angles are equal to are supplementary to each other or equal to each other.
In geometry, a quadrilateral inscribed in a circle, also known as a cyclic quadrilateral or chordal quadrilateral, is a quadrilateral with four vertices on the circumference of a circle. In a quadrilateral inscribed circle, the four sides of the quadrilateral are the chords of the circle.
The opposite angles in a cyclic quadrilateral are supplementary. i.e., the sum of the opposite angles is equal to 180˚.
If e, f, g, and h are the inscribed quadrilateral’s internal angles, then
e + f = 180˚ and g + h = 180˚
by theorem the central angle = 2 x inscribed angle.
∠COD = 2∠CBD
∠COD = 2b
∠COD = 2 ∠CAD
∠COD = 2a
now,
∠COD + reflex ∠COD = 360°
2e + 2f = 360°
2(e + f) =360°
e + f = 180°.
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