Answer:
[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,
