15+ points for !

1. these two triangles are similar by the ∠s.

what is the measure of ∠s?

(remember, these are isosceles triangles.)

[see attachment]

a. 51°

b. 39°

c. 102° < my answer

d. 78°

2. what is the degree measure of ∠b?

[same attachment]

a. 78°

b. 102°

c. 39° < my guess

d. 51°

You are completely right! Good job.
I will explain why;
A. The question states that the triangles are similar, meaning that all corresponding angles are equal and that all the corresponding sides have the same ration. 
It already states the angle of S, which is 102.

B. You know the values of the other angles, and you know the angle sum is 180.
so, 
180-102-39=39
Therefore, this is 39.