Hello, JacobFischer!
Let = angle A.
We will calculate all the angles in the diagram.
Write these figures in your diagram as we go along.
Since is isosceles,
Since is an exterior angle,
Since is isosceles,
Then
Hence,
Since is isosceles,
Then
Hence,
Since is isosceles,
Hence, .[1]
But we know that:
. . That is: . .[2]
Substitute [1] into [2]: .
. . and we have: .