In the given figure DE||DC find x.
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Step-by-step explanation:
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Answered by
1
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.
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