Question

Lines DE and AB intersect at point What is the value of x?C.

Answer 1

Given:

Lines DE and AB intersect at point C.

$m\angle ACE=(2x+2)^\circ$

$m\angle ECB=(5x+3)^\circ$

To find:

The value of x.

Solution:

In the given figure it is clear that the angles $\angle ACE$ and $\angle ECB$ are lie on a straight line AB.

$m\angle ACE+m\angle ECB=$               [Linear pair]

$(2x+2)^\circ+(5x+3)^\circ=180^\circ$

$(7x+5)^\circ=180^\circ$

$7x+5=180$

Subtract 5 from both sides.

$7x=180-5$

$7x=175$

Divide both sides by 7.

$x=\dfrac{175}{7}$

$x=25$

Therefore, the correct option is B.