find X 2 find AB 4xy C D 3x A 5 Solution1 Given 4x 4yy 4x

find X?
2, find AB

Solution

1.

Given <CAB = < ACD

Since the Alternate angles of Transversal AC of Lines CD and AB are equal , we can infer that AB // CD

Similarly since <CAD = < ACB

Alternate angles of Transversal AC of lines AD and CB are equal , we can infer that AD // BC

Thus since AB//CD and AD// BC, ABCD is a parallelogram and length of its opposite sides are equal

AB = CD

=> 4x+y = 4y

=> 4x = 4y-y

=> 4x = 3y

=> x = 3y/4 ................ equation 1

Similarly AD = BC

=> 3x = y+5

=> x = (y+5)/3 .....................equation 2

From equations 1 and 2

=> 3y/4 = (y+5)/3

=> 9y = 4(y+5)

=> 9y = 4y+ 20

=> 9y-4y = 20

=> 5y = 20

=> y = 20/5

=> y = 4

Substitute y = 4 in equation 1

x = 3y/4

=> x = (3*4)/4 =12/4

=> x = 3

2.

AB = 4y = 4*4 =16

Therefore AB = 16