Question

in the given figure if a b parallel to CD then find the value of x

Answer 1

Answer:

in AOB and DOC

<BAO = DCO ( ALternate)

<ABO = <CDO( alternate)

So AA

AOB ~ COD

AO/OC = OB/OD

4/(4X-2) = x+1)/(2x+4)

8x + 16 = 4x^2 + 4x - 2x- 2

4x^2 - 6x -18 = 0

2x^2 - 3x -9 = 0

2x^2 -6x +3x-9=0

2x( x-3) +3( x-3) = 0

(2x+3)( x-3)= 0

x= -3/2, 3

neglect -3/2

So x= 3

Answer 2

Given:

In the given figure ab is parallel to CD

To Find:

Find the value of x.

Solution:

In ΔAOB and ΔDOC,

∠BAO = ∠DCO         ( Alternate angles)

∠ABO = ∠CDO         ( Alternate angles )

∠AOB = ∠COD         ( Vertically opposite angles)

So, by AAA

ΔAOB ~ ΔCOD

So,

AO/OC = OB/OD

4/(4x - 2) = (x + 1)/(2x + 4)

8x + 16 = 4x² + 4x - 2x- 2

4x² - 6x -18 = 0

2x² - 3x -9 = 0

2x² - 6x + 3x - 9 = 0

2x(x-3) + 3( x-3) = 0

(2x+3)( x-3)= 0

x= -3/2, 3  (reject -3/2)

So, x= 3

Hence, the value of x = 3.