Will recommend to see attached picture as name of angles are based on it.
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We can only find value of x if both triangles i.e triangle DOC and triangle AOB are similar.
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[tex]\sf \underline{In \: \triangle \: DOC \: and \: \triangle\:AOB: }[/tex]
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[tex] \sf1. \angle DOC = \angle AOB[/tex]
Reason :-
VOC (Vertically opposite angle)
How to recognize either it is VOC (Vertically opposite angle) or not?
So it's basically very easy to recognize, when ever u see lines intersect each other just like a multiply sign ( × ) either horizontal or parallel they are considered as VOC ans are always equal.
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[tex] \sf2. \angle CDO = \angle BAO[/tex]
Reason:-
Both are of 90°.
So how we recognized that these both angles were in 90°?
When ever you see that angle is marked in square ( □ ) like shape instead of curve shape then it means the angle is 90°.
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[tex]\sf\triangle \: DOC\simeq \triangle\:AOB: [/tex]
By :- AA (angle angle)
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Now Finally Let's find value of x.
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[tex] \dashrightarrow \sf\dfrac{DC}{AB} = \dfrac{OC}{OB} = \dfrac{OD}{OA} [/tex]
Reason :- Corresponding sides of similar triangle are in proportion.
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So:-
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[tex] \dashrightarrow \sf\dfrac{DC}{AB} = \dfrac{OC}{OB}[/tex]
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[tex] \dashrightarrow \sf\dfrac{2}{3.5} = \dfrac{4}{x}[/tex]
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[tex] \dashrightarrow \sf\dfrac{3.5}{2} = \dfrac{x}{4}[/tex]
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[tex] \dashrightarrow \sf\dfrac{35}{2 \times 10} = \dfrac{x}{4}[/tex]
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[tex] \dashrightarrow \sf\dfrac{ \cancel{35}}{2 \times \cancel{10}} = \dfrac{x}{4}[/tex]
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[tex] \dashrightarrow \sf\dfrac{7}{2 \times 2} = \dfrac{x}{4}[/tex]
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[tex] \dashrightarrow \sf\dfrac{4 \times 7}{2 \times 2} = x[/tex]
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[tex] \dashrightarrow \sf\dfrac{ \cancel4 \times 7}{\cancel2 \times 2} = x[/tex]
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[tex] \dashrightarrow \sf\dfrac{ 2 \times 7}{1 \times 2} = x[/tex]
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[tex] \dashrightarrow \sf\dfrac{\cancel 2 \times 7}{1 \times \cancel2} = x[/tex]
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[tex] \dashrightarrow \sf\dfrac{1 \times 7}{1 \times 1} = x[/tex]
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[tex] \dashrightarrow \sf\dfrac{7}{1 } = x[/tex]
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[tex] \dashrightarrow \sf7= x[/tex]
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[tex] \dashrightarrow \bf x = 7[/tex]
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.°. length of x is equal to 7(unit)
