Respuesta :

iciclepiano18

Answer:

[tex]x=6[/tex]

Step-by-step explanation:

Using the given measurements of the angles and the lengths of the sides, we can determine that this figure must be a rectangle.

Diagonals of a rectangle are always equivalent/congruent.

We can use this information to set up an equation:

[tex]DF=EG\\7x-3=5x+9[/tex]

Add 3 to both sides:

[tex]7x-3+3=5x+9+3\\7x=5x+12[/tex]

Subtract 5x from both sides:

[tex]7x-5x=5x-5x+12\\2x=12[/tex]

Divide both sides by 2

[tex]\frac{2x}{2}=\frac{12}{2}\\x=6[/tex]

Answer:

  • 6

[tex] \: [/tex]

Step-by-step explanation:

A rectangle is a parallelogram with equal angles and the diagonals of a rectangle are of equal length.

[tex] \: [/tex]

Therefore,

[tex] \\ { \longrightarrow \qquad{ \sf{ \pmb {DF = EG}}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ \sf{ \pmb {7x - 3 = 5x + 9}}}} \: \: \\ \\[/tex]

Subtracting 5x from both sides we get :

[tex] \\ { \longrightarrow \qquad{ \sf{ \pmb {7x - 5x - 3 = 5x - 5x + 9}}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ \sf{ \pmb {2x - 3 = 9}}}} \: \: \\ \\[/tex]

Adding 3 to both sides we get :

[tex] \\ { \longrightarrow \qquad{ \sf{ \pmb {2x - 3 + 3 = 9 + 3}}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ \sf{ \pmb {2x = 12}}}} \: \: \\ \\[/tex]

Dividing 2 from both sides we get :

[tex] \\ { \longrightarrow \qquad{ \sf{ \pmb { \frac{2x}{2} = \frac{12}{2} }}}} \: \: \\ \\[/tex]

[tex]{ \longrightarrow \qquad{ \frak{ \pmb {x = 6}}}} \: \: \\ \\[/tex]

Therefore,

  • The value of x is 6

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