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If m widehat(VQ)=(y+7)^(@),m widehat(QR)=(x+11)^(@),m widehat(RS)=(3y)^(@), and m widehat(ST)=65^(@), find the values of x and y.

1111. If mVQundefined=(y+7)∘,mQRundefined=(x+11)∘,mRSundefined=(3y)∘ m \widehat{V Q}=(y+7)^{\circ}, m \widehat{Q R}=(x+11)^{\circ}, m \widehat{R S}=(3 y)^{\circ} , and mSTundefined=65∘ m \widehat{S T}=65^{\circ} , find the values of x x and y y .

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Full solution

Q. 1111. If mVQundefined=(y+7)∘,mQRundefined=(x+11)∘,mRSundefined=(3y)∘ m \widehat{V Q}=(y+7)^{\circ}, m \widehat{Q R}=(x+11)^{\circ}, m \widehat{R S}=(3 y)^{\circ} , and mSTundefined=65∘ m \widehat{S T}=65^{\circ} , find the values of x x and y y .
  1. Identify Consecutive Angles: Since VQVQ, QRQR, RSRS, and STST are consecutive angles in a polygon, their measures should add up to 360°360° because it's a full circle.\newlineSo, we have the equation: (y+7)+(x+11)+(3y)+65=360(y+7) + (x+11) + (3y) + 65 = 360.
  2. Set Up Equation: Now, let's simplify the equation: 4y+x+83=3604y + x + 83 = 360.
  3. Simplify Equation: Subtract 8383 from both sides to isolate the terms with variables: 4y+x=2774y + x = 277.
  4. Isolate Variables: We don't have enough information to solve for xx and yy with just one equation, we need another relationship or equation.

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