Question

1. x = m∠aed =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. $\angle AED$ and $\angle BEC$ are vertical angles. So $4x - 40=x + 50$.

Step2: Solve the equation for $x$

Subtract $x$ from both sides: $4x-x-40=x - x+50$, which simplifies to $3x-40 = 50$.
Then add 40 to both sides: $3x-40 + 40=50 + 40$, getting $3x=90$.
Divide both sides by 3: $x=\frac{90}{3}=30$.

Step3: Find the measure of $\angle AED$

Substitute $x = 30$ into the expression for $\angle AED$. $\angle AED=4x-40$. So $\angle AED=4\times30-40=120 - 40 = 80^{\circ}$.

Answer:

$x = 30$, $m\angle AED=80^{\circ}$