Question

note: angles not necessarily drawn to scale.
x =

Explanation:

Step1: Recall angle - sum property at a point

The sum of angles around a point is $360^{\circ}$.

Step2: Identify known angles

We know that one angle is $80^{\circ}$ and another is $20^{\circ}$. Also, since $\angle FEG$ is a straight - line angle, $\angle FEG = 180^{\circ}$.

Step3: Set up the equation

$x+80 + 20=180$ (because the non - overlapping angles on one side of the straight line $FG$ must sum to $180^{\circ}$).

Step4: Solve for $x$

Subtract 80 and 20 from both sides of the equation: $x=180-(80 + 20)$.
$x = 80$.

Answer:

$80$