Given:
Lines DE and AB intersect at point C.
[tex]m\angle ACE=(2x+2)^\circ[/tex]
[tex]m\angle ECB=(5x+3)^\circ[/tex]
To find:
The value of x.
Solution:
In the given figure it is clear that the angles [tex]\angle ACE[/tex] and [tex]\angle ECB[/tex] are lie on a straight line AB.
[tex]m\angle ACE+m\angle ECB=[/tex] [Linear pair]
[tex](2x+2)^\circ+(5x+3)^\circ=180^\circ[/tex]
[tex](7x+5)^\circ=180^\circ[/tex]
[tex]7x+5=180[/tex]
Subtract 5 from both sides.
[tex]7x=180-5[/tex]
[tex]7x=175[/tex]
Divide both sides by 7.
[tex]x=\dfrac{175}{7}[/tex]
[tex]x=25[/tex]
Therefore, the correct option is B.