1. use the following image to answer the questions.
(a) how are the triangles similar? justify your answer with a theorem or postulate.
(b) what is the value of x? show your work.

(a) They are similar because their corresponding angles are congruent. For both triangles, we've been given 2 of the corresponding angles as congruent and therefore the 3rd corresponding angle also has to be congruent. (b) x = 5 First, let's get the length of side AC. Because the triangles are similar, the ratio, 24/32 = Z/28 will hole true. So let's solve for Z to get the length: 24/32 = Z/28 28*24/32 = Z 672/32 = Z 21 = Z Now we know the value of 3x + 6 is 21. So let's set them equal and solve for x. 3x + 6 = 21 3x = 15 x = 5