| In the given figure, if \[AB\left\| DC \right.,\] find the value of x. |
 |
A) 5
B) 7
C) 6
D) 4
Correct Answer: B
Solution :
| [b] Given \[AB||DC\] |
| \[\therefore \,\,\,\angle ODC=\angle OBA\](Alternate interior angles) |
| and \[\angle OCD=\angle OAB\] |
| (Alternate interior angles) |
| \[\therefore \,\,\,\,\,\,\,\Delta DOC\tilde{\ }\Delta BOA\] |
| (By AA similarity criterion) |
| \[\therefore \,\,\,\,\,\frac{OD}{OB}=\frac{OC}{OA}\Rightarrow \frac{x-2}{x-1}=\frac{x+3}{x+5}\] |
| \[\Rightarrow \,\,\,\,\,(x-2)\,(x+5)=(x+3)\,\,(x-1)\] |
| \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,{{x}^{2}}+3x-10={{x}^{2}}+2x-3\,\,\Rightarrow \,\,x=7\] |
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