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ktreyb
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

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