:why does the aa similarity theorem only need to identify the measurement of 2 congruent angles? why is it not necessary to find the measurement of the third angle and show that it is also congruent to the corresponding third angle of a similar triangle?

According to the third angle theorem states if two angles are congruent to two angles in another triangle, the third angles are congruent too. Because a triangle has 180 degrees the third angle in any triangle is 180 degrees  minus the other two angle measures

The answer would be option 4