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Lines DE and AB intersect at point What is the value of x?C.
O 12
25
А.
|(2x + 2)E
38
С
(5x + 3)
52
D
B
I’m sorry if doesn’t make sense but there’s the picture!!

Lines DE And AB Intersect At Point What Is The Value Of XC O 12 25 А 2x 2E 38 С 5x 3 52 D B Im Sorry If Doesnt Make Sense But Theres The Picture class=

Sagot :

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.

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