wxyz is a cyclic quadrilateral prove that wzy+wxy =180
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Given :- ABCD is a cyclic quadrilateral of a circle with centre at O.
To prove :- ∠BAD+∠BCD=180°
∠ABC+∠ADC=180°
Chord AB
∠5=∠8.....(1) [Angle in same segment are equal]
Chord BC
∠1=∠6.....(2) [Angle in same segment are equal]
Chord CD
∠2=∠4.....(3) [Angle in same segment are equal]
Chord AD
∠7=∠3.....(4) [Angle in same segment are equal]
By angle sum property of qudrilateral
∠A+∠B+∠C+∠D=360°
∠1+∠2+∠3+∠4+∠7+∠8+∠5+∠6=360°
(∠1+∠2+∠7+∠8)+(∠3+∠4+∠5+∠6)=360°
(∠1+∠2+∠7+∠8)+(∠7+∠2+∠8+∠1)=360° [From (1), (2) ,(3) and (4)]
2(∠1+∠2+∠7+∠8)=360°
∠BAD+∠BCD=180°
Similarly,
∠ABC+∠ADC=180°
Hence proved .
I've taken a quadrilateral ABCD you can take it as WXYZ and solve it
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