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Find the measure of arc PS

Find the measure of arc PS-example-1
User Domecraft
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Answer:

  • 142°

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Both angles PQS and PRS intercept same arc PS, hence they have same measure:

  • m∠PQS = m∠PRS

Substitute values and solve for x:

  • 5x + 1 = 8x - 41
  • 8x - 5x = 1 + 41
  • 3x = 42
  • x = 14

Plug in the value of x into either angle measure:

  • m∠PQS = 5*14 + 1 = 71°

The intercepted arc is twice the inscribed angle measure:

  • mPS = 2*m∠PQS
  • mPS = 2*71°
  • mPS = 142°
User Heart
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