ABCD is a quadrilateral in which the bisectors ofmeet DC produced at Y

1.	ABCD is a quadrilateral in which the bisectors ofmeet DC produced at Y and BA produced at X respectively8,A and < C
Answer» In the ΔABY: ∠Y + ∠A /2 + ∠B = 180°In the ΔDCX: ∠D +∠C /2 + X = 180° Add them to get: (∠A +∠C)/2 +∠B +∠D +∠X +∠Y = 360° we know∠A + ∠B +∠C + ∠D = 360° From these two equations , we get: angle X+ ∠Y = (∠A+∠C) /2

ABCD is a quadrilateral in which the bisectors ofmeet DC produced at Y and BA produced at X respectively8,A and < C

Answer»

In the ΔABY: ∠Y + ∠A /2 + ∠B = 180°In the ΔDCX: ∠D +∠C /2 + X = 180°

Add them to get: (∠A +∠C)/2 +∠B +∠D +∠X +∠Y = 360° we know∠A + ∠B +∠C + ∠D = 360°

From these two equations , we get: angle X+ ∠Y = (∠A+∠C) /2