Question

google classroom microsoft teams note: angles not necessarily drawn to scale. $x = square^{circ}$

Explanation:

Step1: Recall vertical - angle property

Vertical angles are equal. $\angle AEC$ and $\angle BED$ are vertical angles, so $\angle AEC=\angle BED = 20^{\circ}$.

Step2: Use the fact that angles on a straight - line sum to 180°

$\angle AEC+\angle CEG+\angle GEF+\angle FED = 180^{\circ}$. We know $\angle FED = 50^{\circ}$ and $\angle AEC = 20^{\circ}$, and $\angle GEF = 90^{\circ}$ (since angles on a straight - line). Let $\angle CEG=x$. Then $20 + x+90 + 50=180$.

Step3: Solve for $x$

$20+x + 90+50=180$
$x+160 = 180$
$x=180 - 160$
$x = 20$

Answer:

$20$