MathMatrix

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We’re required to prove that the sum of opposite angles of a cyclic quadrilateral is 180°.

For this, we use Central Angle Theorem.

Proof:

Consider a Centre of the circle, Say O

Join Vertex A and C to center O

Consider minor ∠AOC

∠AOC=2∠D (Central Angle Theorem)

Let ∠AOC = x

Hence, ∠D becomes  x/2

Major ∠AOC becomes 360-x

By Central Angle Theorem:

∠B =  (360-x)/2

∠B = 180-(x/2)

Now, upon adding ∠B & ∠D, we get,

  ∠B + ∠D

=180 – (x/2) + (x/2)

=180°

That’s our answer!!

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