Math, asked by smarikabastakoti8, 7 months ago

wxyz is a cyclic quadrilateral prove that wzy+wxy =180

Answers

Answered by angela1203
1

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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