Triangle QST is an isosceles triangle. You can tell because two of the legs are congruent. Thus angle T is also an x-variable.
Add all of the degrees together, set them equal to 180 and solve for x.
x + x + 74 = 180
2x + 74 = 180
2x = 180 - 74
2x = 106
x = 53
This rules out options C and D.
Now we have to find angle PQS:
The measurements of triangle PQR are congruent to each other so 180 / 3 = 60 they are all 60 degrees.
Angles PQR, PQS, and SQT are in line with each other so they add up to 180.
60 + PQS + 74 = 180
134 + PQS = 180
PQS = 180 - 134
PQS = 46
Triangle PQS is another isosceles triangle. Thus, the two base angles are the same. We are going to add them together plus y and set it all equal to 180 to solve.
46 + 46 + y = 180
92 + y = 180
y = 180 - 92
y = 88
x = 53, y = 88. Your answer is option B
