lines de and ab intersect at point c. what is the value of x? (2x + 2)° (5x + 3)° 12 25 38 52

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. $\angle ACE$ and $\angle BCD$ are vertical angles, so $2x + 2=5x+3 - 180$ (assuming these are supplementary vertical - angle pairs formed by a straight - line intersection). In the case of non - supplementary vertical angles, $\angle ACE$ and $\angle BCD$ are equal, so $2x + 2=5x - 3$.

Step2: Solve the equation for x

First, move the x terms to one side and the constants to the other side. Subtract $2x$ from both sides: $2 = 5x-2x - 3$. Then simplify to get $2 = 3x-3$. Add 3 to both sides: $2 + 3=3x$, so $5 = 3x$. Divide both sides by 3, we get $x=\frac{5}{3}$ which is incorrect. Let's assume they are supplementary angles. So $2x + 2+5x + 3=180$. Combine like terms: $7x+5 = 180$. Subtract 5 from both sides: $7x=180 - 5=175$. Divide both sides by 7: $x = 25$.

Answer:

25