Question

In the given figure, if AB is parallel to DC, find the value of x

Answer 1

Answer:

The value of x is 7.

Step-by-step explanation:

Given information: AB || DC.

In triangle AOB and COD,

$\angle AOB=\angle COD$                  (Vertically opposite angles)

$\angle OBA=\angle ODC$                  (Alternate interior angles)

$\angle OAB=\angle OCD$                  (Alternate interior angles)

By AA rule of similarity,

$\triangle AOB\sim\triangle COD$

The corresponding sides of two similar triangles are proportional.

$\frac{OA}{OC}=\frac{OB}{OD}$

$\frac{x+5}{x+3}=\frac{x-1}{x-2}$

$(x+5)(x-2)=(x-1)(x+3)$

$x^2+5x-2x-10=x^2+3x-x-3$

$3x-10=2x-3$

$3x-2x=-3+10$

$x=7$

Therefore the value of x is 7.

Answer 2

Step-by-step explanation:

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