If a:b = 2:3, find b.


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Answer:

108°

Step by Step Explanation:
  1. Since, both a and b lie on a straight line, we can say that the sum of a and b is equal to 180.
  2.  
    a
    b
      =  
    2
    3
      , cross multiplying the fractions, we get, 2b = 3a, or b =  
    3a
    2
     .
  3. On substituting this value in a + b = 180, we get: a +  
    3a
    2
      = 180, or  
    5a
    2
      = 180, or a = 180 ×  
    2
    5
      , or a = 72 degree.
  4. On substituting this value in a + b = 180, we get:
    72 + b = 180
So,  b = 180 - 72
     b = 108°
    .
  5. Hence, the values of the asked angles a and b are 72° and 108° respectively.

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