CBD = 90° + (a° + b°)/2
We know the following about angle CBD.
1. measurement of interior angle at vertex B is b°
2. measurement of exterior angle at vertex B is (360° - b°)
3. measurement of angle CBD is (360° - b°)/2
Now what we need to do is determine what b is using just a and c.
Since ABC is a triangle and the sum of the interior angles on a triangle add to 180°, we can easily make the following equation
b° = 180° - a° - b°
So let's substitute that equation for b in the expression in #3 above, giving
m = (360° - (180° - a° - b°))/2
And simplify
m = (360° - (180° - a° - b°))/2
m = (360° - 180° + a° + b°)/2
m = (180° + a° + b°)/2
m = 90° + (a° + b°)/2
So the measurement of angle CBD is 90° + (a° + b°)/2
