Hello, gracey!
You left out something in the diagram.
I'll take a guess at what you meant.
Given: .$\displaystyle \angle A = 43^o,\;AB = BC,\;{\color{blue}CD = DE}\;\;{\color{red}?}$
Find: .$\displaystyle \angle g$
Code:
B
o
* *
* *
* *
* 43° 43° *
A o * * * * o * * * o E
C * 43° g *
* *
* *
o
D
Since $\displaystyle \Delta ABC$ is isoscles: .$\displaystyle \angle BCA \,=\,\angle A \,=\,43^o$
Since $\displaystyle \angle BCA$ and $\displaystyle \angle ECD$ are vertical angles: .$\displaystyle \angle ECD \,=\,43^o$
Since $\displaystyle \Delta CDE$ is isosceles: .$\displaystyle \angle g \,=\,\angle ECD \,=\,43^o$