Question

lines de and ab intersect at point c.
what is the value of x?
○ 12
○ 25
○ 38
○ 52
the angles formed are $(2x + 2)^\circ$ and $(5x + 3)^\circ$

Explanation:

Step1: Identify supplementary angles

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

Step2: Combine like terms

Add the variable and constant terms on the left side.
$$7x + 5 = 180$$

Step3: Isolate the variable term

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

Step4: Solve for x

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

Answer:

25