Answer:
see explanation
Step-by-step explanation:
∠ PTS = ∠ NST are vertical angles and are congruent , then
19x + 5 = 17x + 15 ( subtract 17x from both sides )
2x + 5 = 15 ( subtract 5 from both sides )
2x = 10 ( divide both sides by 2 )
x = 5
Then
∠ NST = 17x + 15 = 17(5) + 15 = 85 + 15 = 100° , so
∠ MSR = ∠ NST = 100° ( vertical angles )
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∠ STQ and ∠ NST are same- side interior angles and sum to 180° , then
∠ STQ + 100° = 180° ( subtract 100° from both sides )
∠ STQ = 80°
