Question

I need help with this question. I got it wrong so now I have to go over it and fix it.

Answer 1

We know that:

The following property holds:

$x=\frac{a+b}{2}$

Now, from the figure of the problem, using the previous property we say that:

$\angle\text{AEC }=\frac{AC+BD}{2}$

But:

$\begin{gathered} AC=110 \\ BD=40 \end{gathered}$

Finally:

$\begin{gathered} \angle\text{AEC }=\frac{110+40}{2}=\frac{150}{2} \\ \therefore\angle\text{AEC }=75\degree \end{gathered}$