The Broom Riddle (Solution) ft. Kurt Hugo Schneider part 3/3

Using linear algebra to solve the last one, pretty neat stuff. Let A B C be the vector corresponding to each angle. Then by doing some vector addition and stuff, it is infact A+B=2C which shows that vector C is just basically a linear combination of vector A and vector B which means they lie on the same span or in other word, vector A+B is just vector C but scaled by factor of 2. This indicate that their angle is the same since they are basically the same vector, hence a+b=c