Pedro was curious if circles a and b with x and y Being on a circle respectively with similar so he tried to math one figure onto the other using rigid transformation

The strategy Pedro tend to do isn't worth, because using rigid transformation to place on figure onto the other won't prove that those figures are similar, but it would prove if they are congruent.

Remember that similarity is about proportionality between dimensions of those figures, so it's not about congruence. That means the figures won't match when we place one onto the other.

To prove similarity, Pedro should divide each pair of corresponding coordinate, if all divisions give the same result, that means those figures are similar.

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.