@The-Rogue-Blade

Ah! Good question! It's because you want to look for the "X" in the diagram. The "X" will tell you which two angles go together in the equation given in the video.

The arcs \((80 - a)\) and \(a\) are both inscribed by the "X." This is why we found that the angle \(40^{\circ}\) was the average of \(a\) and \(80-a.\)

However, the arc \(b\) and the arc \((80-a)\) aren't inscribed by two chords which intersect in an "X."

Instead, the arc \(b\) pairs with the arc \(c,\) to form an "X." Thus, the following would be true:

$$ \frac{b + c}{2} = 70^{\circ} $$