Question

in fig of b and p of a quadrilateral ABCD meet CD and p and q respectively p that R+Q=1/2 (ABC+ADC)​

Answer 1

I triangle PBC we have a)

P+4+C=180

P+1/2+B+C=180

IN TRIANGLE OAD we have

Q+A+1=180

Q+A+1/2 D=180 b)

adding a and b we get

P +Q+A+C+1/2B+1/2D=360 C)

BUT IN QUADRILATERAL ABCD WE HAVE

A+B+C+D=360 D)

FROM C AND D WE HAVE

P+Q+A+C+1/2 (B+D)=1

A+B+C+D

P+Q=1/2 (ABC+ADC)HENCE PROVED