Answer :

Answer:

  • m∠RQS = 106°
  • m∠TQS = 74°

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Use angle addition postulate:

  • m∠RQT = m∠RQS + m∠TQS

Substitute the values and solve for x:

  • 180 = 15x + 1 + 10x + 4
  • 180 = 25x + 5
  • 175 = 25x
  • x = 175/25
  • x = 7

Find the angle measures:

  • m∠RQS = 15*7 + 1 = 106
  • m∠TQS = 10*7 + 4 = 74