Question

lines de and ab intersect at point c.
what is the value of x?
○ 12
○ 25
○ 38
○ 52

Explanation:

Step1: Identify supplementary angles

The angles $(2x+2)^\circ$ and $(5x+3)^\circ$ are supplementary, so their sum is $180^\circ$.
<Expression>$(2x + 2) + (5x + 3) = 180$</Expression>

Step2: Combine like terms

Add the variable terms and constant terms together.
<Expression>$7x + 5 = 180$</Expression>

Step3: Isolate the variable term

Subtract 5 from both sides of the equation.
<Expression>$7x = 180 - 5 = 175$</Expression>

Step4: Solve for x

Divide both sides by 7 to find x.
<Expression>$x = \frac{175}{7} = 25$</Expression>

Answer:

25