Question

how to prove that cyclic quadrilateral have the sum of 180 of it's opposite angles​

Answer 1

Answer:

angleADC =1/2 arcABC

similarly angle ABC = arcADC

hence RHS ARE EQUAL

THEREFORE

angleADC + angleABC =1/2 (arcABC + arcADC)

1/2×360 (SINCE MEASURE OF A CIRLCR IS 360

=180

HENCE PROVED

Answer 2

Answer:

Theorem.

Sum of the opposite angles of a cyclic

quadrilateral is 180°.

But ∠ACB + ∠BAC + ∠ABC =

180° [Sum of the angles of a triangle] ∴ ∠ADC +

∠ABC = 180° ∴ ∠BAD + ∠BCD = 360° – (∠ADC +

∠ABC) = 180°.

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