Question

A quadrilateral can be inscribed in a circle, if and only if, the opposite angles in that quadrilateral are supplementary.

Answer 1

The opposite angles are equal to are supplementary to each other or equal to each other.

What is a Quadrilateral Inscribed in a Circle?

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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