Question

prove that in a given cyclic quadrilateral some of the opposite angles is two right angles and conversely.​

Answer 1

Answer:

WHERE IS THE DIAGRAM ?

THANK YOU

Answer 2

Answer:

To prove: sum of opposite angles of a cyclic quadrilateral is 180

o

Let ABCD is cyclic quadrilateral.

To prove that ∠A+∠C=180° and ∠B+∠D=180°

Construction :Join OB and OD.

We know that ∠BOD=2∠BAD

(The angle at the centre is twice the angle at the circumference )

∠BAD=

2

1

∠BOD

Similarly we can write ∠BCD=

2

1

∠BOD

now add above two equations

∠BAD+∠BCD=

2

1

∠BOD+

2

1

∠DOB

∠BAD+∠BCD=

2

1

(∠BOD+∠DOB) (complete angle)

∠BAD+∠BCD=

2

1

×360°=180°

So we get ∠A+∠C=180°

And similarly ∠B+∠D=180°