prove that opposite angles of a cyclic quadrilateral are supplementary​

2 thoughts on “prove that opposite angles of a cyclic quadrilateral are supplementary​”

1. Step-by-step explanation:

   The opposite angles in a cyclic quadrilateral are supplementary. i.e., the sum of the opposite angles is equal to 180˚.

   Consider the diagram below.

   If a, b, c, and d are the inscribed quadrilateral’s internal angles, then

   a + b = 180˚ and c + d = 180˚.

   Let’s prove that;

   a + b = 180˚.

   Join the vertices of the quadrilateral to the center of the circle.

   Recall the inscribed angle theorem (the central angle = 2 x inscribed angle).

   ∠COD = 2∠CBD

   ∠COD = 2b

   Similarly, by intercepted arc theorem,

   ∠COD = 2 ∠CAD

   ∠COD = 2a

   ∠COD + reflex ∠COD = 360o

   2a + 2b = 360o

   2(a + b) =360o

   By dividing both sides by 2, we get

   a + b = 180o.

   Hence proved!

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2. [tex]\huge\bold{\mathtt{\red{A{\pink{N{\green{S{\blue{W{\purple{E{\orange{R}}}}}}}}}}}}}[/tex]

   The opposite angles in a cyclic quadrilateral are supplementary. i.e., the sum of the opposite angles is equal to 180˚. Consider the diagram below. a + b = 180˚ and c + d = 180˚.

   Reply