Why doesn't P just open up to the 80 degree angle as an inscribed angle? Would've made things a lot quicker, also doesn't it make sense?

Why doesn't P just open up to the 80 degree angle as an inscribed angle? Would've made things a lot quicker, also doesn't it make sense?

@TheBladeDancer You are right, using the Inscribed Angle Theorem would work a lot faster. That theorem tells us that we can take the difference of the two arcs that are inscribed by angle \(P,\) and divide that by \(2\) to get the measure of \(\angle P.\)
$$ \angle P = \frac{80^{\circ}  30^{\circ}}{2} = \frac{50^{\circ}}{2} = \boxed{25^{\circ}} $$
You've finished the course already and are just reviewing, and so this theorem, which is proved in Day 10, isn't something that the kids know about when they're doing the Day 6 lesson. Maybe that's why Prof. Loh tried to use other methods to solve it! That's my guess, but I also know that Prof. Loh likes to use different solution methods to check his work, also.