Question

in the given figure AB is parallel to DC. find the value of X. it's urgent... please help​

Answer 1

Answer:

Given information: AB || DC.

In triangle AOB and COD,

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

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

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

By AA rule of similarity,

\triangle AOB\sim\triangle COD△AOB∼△COD

The corresponding sides of two similar triangles are proportional.

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

OC

OA

=

OD

OB

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

x+3

x+5

=

x−2

x−1

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

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

2

+5x−2x−10=x

2

+3x−x−3

3x-10=2x-33x−10=2x−3

3x-2x=-3+103x−2x=−3+10

x=7x=7