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m/_PTS=x+67,m/_UTP=x+74, and m/_UTS=133^(@). Find x.

m∠PTS=x+67,m∠UTP=x+74 m \angle P T S=x+67, m \angle U T P=x+74 , and m∠UTS=133∘ m \angle U T S=133^{\circ} . Find x x .

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Full solution

Q. m∠PTS=x+67,m∠UTP=x+74 m \angle P T S=x+67, m \angle U T P=x+74 , and m∠UTS=133∘ m \angle U T S=133^{\circ} . Find x x .
  1. Write Equation: Since PTS, UTP, and UTS form a triangle, their measures should add up to 180180 degrees.\newlineSo, we have the equation x+67+x+74+133=180x + 67 + x + 74 + 133 = 180.
  2. Combine Like Terms: Combine like terms and simplify the equation: 2x+67+74+133=1802x + 67 + 74 + 133 = 180.
  3. Simplify Equation: Add up the numbers: 2x+274=1802x + 274 = 180.

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