Question

ABCD. is a quadrilateral in which the bisectors of angleA and angle C meet DC produced at Y and BA produced at X respectively prove that angleX+angleY=1/2(A+C)​

Answer 1

Answer:

angle X + angle y +1/2 (angle A + angle C)

Step-by-step explanation: in triangle XBC

angle x + angleb + angle 4= 180

angle x+ angle b+1/2 angle c= 180------(i)

in triangle ADY

angle 2+angle D+angle Y=180

1/2 angle a + angle d+angle y= 180------(ii)

adding (I)and (ii)

angle X+ angle y +angle B+ angle D=360

= angle x+angleY +angle B+angle D+1/2angle C+1/2 angleA=angleA+angleB+angleC+angle D

angleX+angleY =angle A-1/2angleA+angleC-1/2angle C

angle X+angleY =(1/2 angle A +angleC)

HENCE PROVED