Question

2.) $angle bec = 7x - 23$ and $angle aed = 2x + 52$. find the measure of x.

Explanation:

Step1: Set the two - angle expressions equal

Assume $\angle BEC$ and $\angle AED$ are vertical angles (vertical angles are equal). So we set up the equation $7x - 23=2x + 52$.

Step2: Isolate the variable terms

Subtract $2x$ from both sides of the equation:
$7x-2x - 23=2x-2x + 52$, which simplifies to $5x-23 = 52$.

Step3: Isolate the variable

Add 23 to both sides of the equation:
$5x-23 + 23=52 + 23$, so $5x=75$.

Step4: Solve for x

Divide both sides of the equation by 5:
$\frac{5x}{5}=\frac{75}{5}$, so $x = 15$.

Answer:

$x = 15$