In a trapezium ABCD if AB|ICD and diagonals intersect at O, prove that

1.	In a trapezium ABCD if AB\|ICD and diagonals intersect at O, prove that AO.OD BO.OC16. The angles of a triangle are x, y and 40Â°. The difference between the twoangles r and y is30Â°. Find r and y
Answer» x-y=30 →equation 1 x+y+40 = 180 (since sum of angles of a triangle = 180) x+y=140 →equation 2 (variables on one side,constants on one side) equation 1 → x-y=30 equation 2 → x+y=140 ⇒ 2x= 170 (∵ -y+y=0) ⇒x = 170/2 ⇒ x = 85 substitute x in equation 1 (or equation 2.its your choice. you'll get the same answer) equation 1 → x-y=30 85-30 = y (substituting x and bringing 30 on one side and y on one side) 55 = y ∴x=85 y=55

In a trapezium ABCD if AB|ICD and diagonals intersect at O, prove that AO.OD BO.OC16. The angles of a triangle are x, y and 40Â°. The difference between the twoangles r and y is30Â°. Find r and y

Answer»

x-y=30 →equation 1

x+y+40 = 180 (since sum of angles of a triangle = 180)

x+y=140 →equation 2 (variables on one side,constants on one side)

equation 1 → x-y=30

equation 2 → x+y=140

⇒ 2x= 170 (∵ -y+y=0)

⇒x = 170/2

⇒ x = 85

substitute x in equation 1 (or equation 2.its your choice. you'll get the same answer)

equation 1 → x-y=30

85-30 = y (substituting x and bringing 30 on one side and y on one side)

55 = y

∴x=85

y=55