Given:
[tex]\begin{gathered} m\angle AEC\text{ = 4x -40} \\ m\angle BED\text{ = x + 50} \end{gathered}[/tex]
Angles AEC and BED are vertically opposite angles. Hence, we can write:
[tex]\begin{gathered} 4x\text{ - 40 = x + 50} \\ \text{Collect like terms} \\ 4x\text{ -x = 50 + 40} \\ 3x\text{ = 90} \\ \text{Divide both sides by 3} \\ \frac{3x}{3}\text{ = }\frac{90}{3} \\ x\text{ = 30} \end{gathered}[/tex]
The number of degrees in angle AEC:
[tex]\begin{gathered} m\text{ }\angle AEC=(4x-40)^0 \\ =\text{ (4 }\times30-40)^0 \\ =(120-40)^0 \\ =80^0 \end{gathered}[/tex]
Answer:
The measure of angle AEC = 80 degrees
