Question

Can somebody help me please

Answer 1

x = 7

Explanation:

The 2 right triangles are similar by the AA postulate, then the ratios of corresponding sides are in proportion, that is

`(x)/(4)` =
`(3.5)/(2)` ( cross- multiply )

2x = 14 ( divide both sides by 2 )

x = 7

Answer 2

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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`\sf \underline{In \: \triangle \: DOC \: and \: \triangle\:AOB: }`

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`\sf1. \angle DOC = \angle AOB`

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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`\sf2. \angle CDO = \angle BAO`

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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`\sf\triangle \: DOC\simeq \triangle\:AOB:`

By :- AA (angle angle)

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Now Finally Let's find value of x.

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`\dashrightarrow \sf(DC)/(AB) = (OC)/(OB) = (OD)/(OA)`

Reason :- Corresponding sides of similar triangle are in proportion.

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So:-

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`\dashrightarrow \sf(DC)/(AB) = (OC)/(OB)`

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`\dashrightarrow \sf(2)/(3.5) = (4)/(x)`

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`\dashrightarrow \sf(3.5)/(2) = (x)/(4)`

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`\dashrightarrow \sf(35)/(2 * 10) = (x)/(4)`

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`\dashrightarrow \sf\frac{ \cancel{35}}{2 * \cancel{10}} = (x)/(4)`

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`\dashrightarrow \sf(7)/(2 * 2) = (x)/(4)`

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`\dashrightarrow \sf(4 * 7)/(2 * 2) = x`

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`\dashrightarrow \sf( \cancel4 * 7)/(\cancel2 * 2) = x`

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`\dashrightarrow \sf( 2 * 7)/(1 * 2) = x`

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`\dashrightarrow \sf(\cancel 2 * 7)/(1 * \cancel2) = x`

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`\dashrightarrow \sf(1 * 7)/(1 * 1) = x`

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`\dashrightarrow \sf(7)/(1 ) = x`

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`\dashrightarrow \sf7= x`

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`\dashrightarrow \bf x = 7`

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.°. length of x is equal to 7(unit)