prove that opposite angles of a cyclic quadrilateral are supplementary
Answers
Answered by
2
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˚.
Answered by
0
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!
Similar questions