For 2 triangles to be similar, they have to have congruent angle measures with corresponding sides that exist in proportion to one another. #14 shows a triangle with 2 angle measures given. We can find the third angle in that triangle to be 65. The one on the right in #14 shows a triangle with 66 degrees in the position corresponding to 65 on the left. Those are not similar (we know nothing about the side lengths so we have no choice but to work with the angles).
#15 shows 2 triangles that are "attached" by angle M in the center. Those 2 angles meet to create vertical angles, and vertical angles are congruent, so angle HMG and angle KMJ are congruent. If both triangles have 2 angles that are corresponding and congruent, then the third angles in both will also be guaranteed to be congruent. So those 2 triangles are similar by AA
