Question

opposite angle of cyclic quadrilateral is supplementary prove​

Answer 1

Answer:

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°. Hence proved. Converse of this theorem is also true.

Answer 2

Answer:

❀given:

let ABCD is cyclic quadrilateral

❀ To Prove:

∠A+ ∠C=180° and ∠B+∠D=180°

❀proof:

∠BOD=2 ∠BAD

∠BAD=$\frac{1}{2}$∠BOD

Similarly ∠BCD=$\frac{1}{2}$∠DOB

∠BAD +∠BCD=$\frac{1}{2}$∠BOD+$\frac{1}{2}$∠DOB

=$\frac{1}{2}$(∠BOD+∠DOB)

=($\frac{1}{2} )$×360°=180°

similarly ∠B+∠D=180°