In the figure shown, PQ¯--> is perpendicular to QR¯--> and ST¯--> is parallel to QR¯-->. The measure of ∠SQR--> is 45°; the measure of ∠TQR--> is 30°; and QS=50-->. What is the perimeter of triangle SQT?

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Problem Solving questions are mixed in with Data Sufficiency questions to make up the 37 questions of the GMAT Quantitative section, which must be completed in 75 minutes. The Problems You’ll Work On When working through the problem solving questions test your understanding of: Basic math, including fractions, decimals, ratios and proportions, percents, and exponents. Probability and Statistics, including counting techniques, permutations and combinations, basic probability, arithmetic mean, median, mode, and standard deviation. Algebra, including polynomials, linear equations and... Show more

In the figure shown, <img><m:mrow><m:mover accent='true'><m:mrow><m:mi>P</m:mi><m:mi>Q</m:mi></m:mrow><m:mo stretchy='true'>¯</m:mo></m:mover></m:mrow></m:math>--> is perpendicular to <img><m:mrow><m:mover accent='true'><m:mrow><m:mi>Q</m:mi><m:mi>R</m:mi></m:mrow><m:mo stretchy='true'>¯</m:mo></m:mover></m:mrow></m:math>--> and <img><m:mrow><m:mover accent='true'><m:mrow><m:mi>S</m:mi><m:mi>T</m:mi></m:mrow><m:mo stretchy='true'>¯</m:mo></m:mover></m:mrow></m:math>--> is parallel to <img><m:mrow><m:mover accent='true'><m:mrow><m:mi>Q</m:mi><m:mi>R</m:mi></m:mrow><m:mo stretchy='true'>¯</m:mo></m:mover></m:mrow></m:math>-->. The measure of <img><m:mrow><m:mo>∠</m:mo><m:mi>S</m:mi><m:mi>Q</m:mi><m:mi>R</m:mi></m:mrow></m:math>--> is 45°; the measure of <img><m:mrow><m:mo>∠</m:mo><m:mi>T</m:mi><m:mi>Q</m:mi><m:mi>R</m:mi></m:mrow></m:math>--> is 30°; and <img><m:mrow><m:mi>Q</m:mi><m:mi>S</m:mi><m:mo>=</m:mo><m:mn>50</m:mn></m:mrow></m:math>-->. What is the perimeter of triangle <em>SQT</em>? <br><img src='https://www.fatskills.com/images2/GMAT/9781119363125-fg0317.png' alt='image'>