We are told that the given figures are similar, and we want to find the values of x and y for the missing angle values. Let's analyze the given polygons.
Since we are given that A B C D ~ Q S R P, we can identify the pairs of congruent angles by matching them using the order they appear in the similarity statement.
ccccc
A & B & C & D
↓ & ↓ & ↓ & ↓
Q & S & R & P
Let's highlight the corresponding vertices and angles on the graph.
With this information, we can write two equations. One equation in terms of x and the other in terms of y.
(x+34)°&= 97°
(3y-13)°&= 83°
Now we can use these relations to solve for the values of x and y. Let's start with x.
