Suppose that m ∠ S = m ∠ O and that m ∠ I = 4 ( m ∠ S ). Find m ∠ I.

Question

Suppose that   m  ∠  S  =  m  ∠  O and that   m  ∠  I  =  4  (  m  ∠  S  ). Find   m  ∠  I.

Winston Cooper · Accepted Answer

Step 1Gives,   m  ∠  s  =  m  ∠  o     a  n  d     m  ∠  i  =  4  (  m  ∠  i  )Find   m  ∠  IStep 2We know thatIn triabgle SOI  m  ∠  s  +  h  ∠  I  =      180          ∘          m  ∠  s  =  m  ∠  o     (  g  i  v  e  n  )    m  ∠  s  +  m  ∠  s  +  m  ∠  i  =      180          ∘          2  m  ∠  s  +  m  ∠  i  =      180          ∘          2  m  ∠  s  +  4  m  ∠  s  =      180          ∘          6  m  ∠  s  =      180          ∘          ∴  m  ∠  s  =      180    6      ∴  m  ∠  s  =      30          ∘          m  ∠  i  =  4  m  ∠  s    m  ∠  i  =  4  ×      30          ∘          =      120          ∘          =  m  ∠  i  =      120          ∘

Suppose that m∠S = m∠O and that m∠I = 4 (m∠S). Find m∠I.

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