Question

If the opposite angle of quadrilateral is supplementary then it is cyclic quadrilateral

Answer 1

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°

Answer 2

Step-by-step explanation:

In a cyclic quadrilateral, the sum of a pair of opposite angles is 180∘ (supplementary).

In a cyclic quadrilateral with vertices A,B,C,D A , B , C , D , sides

a=AB a = A B , b=BC b = B C , c=CD c = C D , and d=DA

d = D A , and diagonals p=AC p = A C and q=BD q = B D .