Hello!
Let's write some important information:
AE = 4x +6
BD = 5x +30
ECB = 40º
AED = ?
First, note that AE is half AC. So, we know that:
[tex]\begin{gathered} AC=2(AE) \\ AC=2(4x+6) \\ \boxed{AC=8x+12} \end{gathered}[/tex]
Now, other important information:
AC is equal to BD, so we can obtain the value of x:
[tex]\begin{gathered} AC=BD \\ 8x+12=5x+30 \\ 8x-5x=30-12 \\ 3x=18 \\ x=\frac{18}{3} \\ \boxed{x=6} \end{gathered}[/tex]
Now, let's remember the definition of vertex opposite angles:
• the sides of these angles are opposite lines and do not share any of the sides;
• these angles are congruent (equal).
So, we also can say that:
[tex]m\angle ECB=m\angle AED=40\degree[/tex]
